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4. Cycle (2005/06)

Thu. 20. Sep. 2007, 14.00-14.45, University of Zürich, PLM 103/104, Plattenstrasse 14

Christer Göransson:
    

Abstract: TBA [more]

Fri. 6. Jul. 2007, 14.00-14.45, University of Zürich, PLM 103/104, Plattenstrasse 14

Regis Houssou
    

Abstract: TBA [more]

Fri. 6. Jul. 2007, 15.00-15.45, University of Zürich, PLM 103/104, Plattenstrasse 14

Anna Rhyner-Solkina
    

Abstract: TBA [more]

Thu. 21. Jun. 2007, 14.00-14.45, University of Zürich, PLD-E-04, Plattenstrasse 32

Gidione Oyebanji
    

Abstract: TBA [more]

Mon. 5. Feb. 2007, 16.00-16.45, University of Zürich, SOE-E-8, Schönberggasse 11

Paul Hughes:
     Modelling dependence in hedge funds

Abstract: TBA [more]

Mon. 5. Feb. 2007, 14.45-15.30, University of Zürich, SOE-E-8, Schönberggasse 11

Vasiliki Mavrou:
     Modeling the dynamics of electricity prices

Abstract: Until the beginning of the 90’s, the uncertainty in electricity prices has been little, since regulators fixed electricity prices as a function of transmission, generation and distribution costs. With the introduction of competition in the supply and generation activities being the main target, many countries are going through a deregulation process in the last years. The UK deregulated in the early 90’s, Alberta on 1st of January 1996 and California on 1st of April 1998. Norway and Sweden founded the Nordic Power Exchange, which is also known as the NordPool ASA. Finland also joined the exchange area and since the 1st October 2000, when Denmark joined as well, all the nordic countries operate on the same market. The grand driving force for the liberalization was the drop of the prices. In a completely competitive market, the production should be more efficient, obliging the prices to tend eventually towards limits that are set by fuel costs. The main consequence of the deregulation is that the electricity prices are determined by the coaction between demand (the agents who buy energy and then sell it to the consumers) and supply (generators)in what is known as a ”pool”. The result is that the suppliers compete in selling electricity in the pool while the agents purchase it from the market pool at prices of equilibrium that are set at a point of intersection of supply and aggregated demand. The main characteristic of the new deregulated prices is that their volatility is extremely high. The deregulation of electricity markets has introduced then more uncertainty within the sector and consequently usual financial facets such as derivative contracts, risk management or hedging are introduced in the electricity sector. The understanding and characterizing of the structure of the electricity prices is essential in the cornerstone of the risk management and valuation of financial claims and real assets on this commodity. In this thesis we investigate the goodness of fit of two models: The first model belongs to the ARMA/GARCH family. We pay special attention to the normality assumption of the innovations and test their fit to the Hyperbolic and Stable laws. The second model is a two-state Markov Regime Switching model assuming that the base regime follows an Ornstein-Uhlenbeck process. For the spike regime we fit three distributions, the Gaussian, the Log-normal and the Pareto. Furthermore, we do a simulation for the Regime-Switching case to generate trajectories and comment on the similarities of the results with the real world data used. [more]

Mon. 5. Feb. 2007, 14.00-14.45, University of Zürich, SOE-F-8, Schönberggasse 11

Yacine Moulay-Rchid:
     Counterparty Risk Modeling of Range Accrual Swaps

Abstract: Counterparty risk is defined as the risk that a counterparty does not fulfill its payment obligations. One of the main drivers of this risk is the exposure at default: the potential value of the derivative portfolio at a certain future point in time. This involves the modelling of risk factors dynamics like interest rates, equity prices, credit spreads, etc. Models from derivatives pricing are then used to revalue the portfolio in the future given the simulated risk factors. This thesis deals with the valuation of range accrual swaps and the derivation of efficient analytical pricing formula for counterparty risk estimation. We present a general valuation framework of range accrual swaps where the pricing is decomposed in terms of delayed digital and asset-or-nothing call options. The pricing of these options is then discussed under the general multifactor Gaussian HJM framework. We give a specific formulation of the pricing under Ho-Lee and Vasicek short rate model. The magnitude of the convexity adjustment terms involved in the pricing of delayed digital options is then discussed. Alternatively, we introduce a pricing formula under BGM model with drift interpolation. We finally present the foundations of static replication pricing methodology and its application to the pricing of range accrual swaps. The analytical pricing obtained is then compared to the Front Office static replication pricing.

Fri. 2. Feb. 2007, ETH Zürich, 14.00-14.45, HG D 3.1, Rämistr. 101

Joachim Connault:
     Stochastic Volatility Models Based on Time Changes

Abstract: The seminal paper in mathematical finance for option pricing is due to [Black & Scholes, 1973] and assume stock price to be continuous and log-normal, more precisely a continuous Gaussian process. It leads to exact calculation and enables to find a close solution for European options. The crucial parameter that drives the latter model is the volatility of the underlying stock process that is assumed to be constant. But this approach is quite restrictive and does not reflect the observable price behaviour. A further approach consists to model the stock process as diffusion with stochastic volatility, whose logarithm follows for example an Ornstein-Uhlenbeck process or a Cox-Ingersoll-Ross process. But such a model requires much more parameters and complicates the calibration procedure. But it does not embed the possibility of jumps, crash that can happen in the real world. A more general approach is to consider jump diffusions. The common justifications are that diffusions help to capture the small moves occurring frequently and the variation in strike at longer terms, while jump diffusions capture the large moves occurring more frequently and the variation in strike at shorter terms. A general L´evy process captures this effects and the possibility of changing the clock multiplies the amount of possible models: we subordinate the L´evy process to a random time change. The principle for asset price modeling is to take an exponential of the L´evy process that is compensated to obtain a martingale. That explains that we will mainly focus on the derivation of the characteristic exponent of time changed L´evy processes. This paper will focus on mathematical properties and modeling. We will not deal with estimation and calibration problems. In the first chapter, we recall some definitions and properties about L´evy processes based on [Bertoin, 1996], and how to build martingales based on L´evy exponentials. In the second chapter we will describe the general properties of time changed processes discussed by [Carr & Wu, 2004] and [Carr et al., 2003]. In the third chapter we expose the Variance Gamma model derived from time changed Brownian exponential and the extended model CGMY. Finally the fourth chapter briefly deals with option pricing. [more]

Tue. 30. Jan. 2007, ETH Zürich, 15.45-16.30, HG D 3.3, Rämistr. 101

Sebastian Matei:
     A Multivariate Jump-Diffusion Model and Pricing of Multi-Currency Options

Abstract: TBA [more]

Tue. 30. Jan. 2007, ETH Zürich, 15.00-15.45, HG D 3.3, Rämistr. 101

Daniel Seiler:
     Backtesting Multiple-Period Forecasting Models-- with Application to Credit Exposure Models

Abstract: Within the Basel II accord financial institutions are free to develop their own internal model for credit risk. The accompanying mandatory model validation obliges to backtest exposure predictions over long forecast horizons such that the forecasted variable is not realised before the next is produced. Due to overlapping forecast horizons, the observations are subject to common shocks that create temporal dependence. This master thesis evaluates different approaches to find an optimal backtest that takes into account this dependence as well as the limited available data. It presents an overview of existing backtests and proposes a new validation procedure for multiple-period forecasting models. With an additional distributional and a stationarity assumption multiple-period density as well as quantile forecasting models can be validated very easily and the data is used very efficiently. Tests for density and quantile predictions are presented and their power properties are analysed. Finally, the proposed tests are applied to credit exposure models and conclusions are drawn. [more]

Mon. 29. Jan. 2007, 17.45-18.30, University of Zürich, Room KOL-N-01/02, Rämistrasse 71

Nicolas Gisiger:
     Portfolio credit derivatives based on rating migration

Abstract: This thesis discusses portfolio credit derivatives which offer rating migration protection on a portfolio of assets. Credit rating migrations are in- teresting, both from an originator's and an investor's point of view. After discussing the possibilities and problems of expressing a view on rating mi- gration through default-sensitive instruments, we introduce a new portfolio credit derivative. Applications and payo® examples are provided, as well as a chapter on the modelling and pricing of the product. [more]

Mon. 29. Jan. 2007, 17.00-17.45, University of Zürich, Room KOL-N-01/02, Rämistrasse 71

Natalia Dolgova:
     Hedging of barrier options

Abstract: The hedging approaches for barrier options in the literature are based on assumptions that make these methods di±cult to implement. Either one requires a not existing excessive liquidity of hedging instruments, or not acceptable sizes of the hedge positions follow or the hedge errors are not acceptable in the crucial barrier price region. Based on these observations we propose a Vega-matching strategy. We show that this approach leads to a better hedging performance in most cases compared to dynamic hedging and static hedging of Derman, Kani and Ergener (1994) and of Carr and Chou (1997a). Since the quality of any static hedge changes over time, we finally define an implementable optimization approach which allows us to control the hedging performance over time. The optimal hedging strategy significantly improves the non-optimized ones. [more]

Fri. 26. Jan. 2007, 10.45-11.30, University of Zürich, Room 103/104, Plattenstrasse 14

Delia Pirnog-Ajtay:
     Foreign Exchange Risk: Pricing and Hedging Exotic Instruments

Abstract: This project discusses exotic instruments used in the Foreign Exchange(FX) markets. An overview of the most popular exotic derivatives is presented, followed by the pricing alternatives of these securities. Hedging methods using static replication for some classes of exotic options are afterward discussed. Finally, risk management control of an active FX portfolio is studied. [more]

Fri. 26. Jan. 2007, 10.00-10.45, University of Zürich, Room 103/104, Plattenstrasse 14

Urs Hasler:
     FX basket options

Abstract: Although, we refute the iid normality assumption for daily and weekly FX returns, we give di®erent approaches to price and hedge mainly European arithmetic as well as geometric basket options under the assumption of iid normal distributed returns. The main goal is to conserve consistency with the initial Black-Scholes assumption of underlying assets follow geometric Brownian motions. On one hand we fit the statistical properties of an arithmetic basket to known distributions where we derive closed-form results for the option price. On the other hand we give a numerical procedure, based on finite diferences, to price European as well as American basket options. As an extension, we introduce so-called Wishart processes from where we derive closed-form solutions for geometric European basket options with stochastic covariance. [more]

Mon. 22. Jan. 2007, ETH Zürich, 16.45-17.30, HG D 3.1, Rämistr. 101

Stefan Plesko:
     Operational Risk Quantification with Extreme Value Theory and Actuarial Methods

Abstract: This paper analyses the quality and applicability of Extreme Value Theory (EVT) for the estimation of high quantiles in the application of Operational Risk. Further the quality of a method popular among practitioners, namely fitting Lognormal tails to extreme data is evaluated. We present a method on how to implement insurance contracts on Operational Risk into the calculation of the total loss distribution and thus quantify the benefit of insurance on Value at Risk numbers. Furthermore the benefit of EVT for single losses on the accuracy of total loss quantile estimations, for the cases with and without insurance, is analysed. We find confirmed that expected EVT quantile estimators overestimate theoret- ical quantiles, which comes from the functional form of the quantile estimator, namely its convexity in ». We are able to asymptotically quantify the bias and compare the empirical bias with the expected asymptotical bias. Further we find that Lognormal tail fitting is not able to yield satisfying results for quantile estimations. We find that the method on how to incorporate insurance contracts described in this paper works well and yields theoretically expected results. Finally, just like in the case of single losses, the quantile estimation on a total loss level becomes more accurate if EVT is used for the tail of a single loss distribution, especially in the case of heavy-tailed distributions. [more]

Fri. 12. Jan. 2007, 15.00-15.45, University of Zürich, Room E6, Plattenstrasse 32

Miret Padovani:
     A flow function model

Abstract: The aim of this thesis is to estimate and analyze the flow function model developed within the research project in evolutionary finance led by Professors Thorsten Hens and Peter W¨ohrmann. The model attempts to explain flows of funds into the Swiss Performance Index. We depart from a joint hypothesis regarding the investment behavior of momentum and value investors. We estimate several possible flow functions representing the external (flow) component of investors' wealth. The results we obtain are supportive of the intuition given by the model. [more]

3. Cycle (2004/05)

Mon. 13. Mar. 2006, ETH Zürich, 10.30-11.15, HG D 3.1, Rämistr. 101

Laurent Cavazzana:
     Wavelet methods for asset pricing under L´evy processes: the valuation of compound options

Abstract: We present a PDE approach for the valuation of compound options. The case of assets driven by L´evy processes is investigate. Arbitrage-free prices u of an european contract on risky assets whose log-returns are modelled by L´evy processes satisfy a parabolic partial integro-differential equation (PIDE). The PIDE is localized to bounded domain and discretized by the µ-scheme in time and a Wavelet Garlekin method with N degrees of freedom in log-price space. The use of the wavelets basis is twofold. Firstly, it allows for a good preconditionning to efficiently solve the linear system in each time step with iterated methods. Secondly, the wavelet basis allows to compress the fully populated matrix for A in a sparse matrix. Numerical examples on european compound call options are presented, in the Black & Scholes setting as well as for the pure jump VG dynamics. [more]

Mon. 13. Mar. 2006, ETH Zürich, 9.30-10.15, HG D 3.1, Rämistr. 101

Robert Robert:
     The Enhanced Tilley Bundling Method: Single and Multiple Underlying Assets

Abstract: As a method for pricing derivative contract, Monte Carlo is seen as the promising alternative to other methods due to various reasons. For many years, most people considered that the method is only suitable for pricing European derivative contracts. Such view was mainly driven by the fact that, unlike its European counterparts, American option allows the option holder to exercise the option at any time prior to maturity. Hence, the pricing problem becomes very complicated as the option holder need to determine the optimal exercise strategy. However, Tilley (1993) dispelled the view. By introducing a simple bundling algorithm to the sample path, the author show how Monte Carlo simulation can be used to price American derivative contract. Despite its simplicity, this method has a major drawback: memory requirement. In the implementation of the algorithm, all the paths need to be stored for the purpose of sorting and bundling. To alleviate this problem, Chan, et. al. (2005) proposed an minor improvement to the original Tilley bundling algorithm which they called Enhanced Tilley bundling. By utilizing of the embedded seed functionality embedded in any random number generator, the Enhanced Tilley algorithm reduces the memory requirement from MN to 0(M). In this report, we will implement the Enhanced Tilley bundling algorithm in single and multiple underlying assets case. The main goal of this paper is to better understand the method because, despite its deficiencies, the algorithm is very suitable for parallel computing which is a major attraction from computational perspective. [more]

Thu. 23. Feb. 2006, ETH Zürich, 17.15-18.00, HG D 5.1, Rämistr. 101

Antonio Del Favero:
     Exercises and Other Educational Material to Accompany the Text "Quantitative Risk Management: Concepts, Techniques and Tools" Part I: Basic Concepts in Risk Management

Abstract: The aim of my master thesis is to complement and enrich with exercises and other educational material the second chapter, entitled “Basic Concepts in Risk Management”, of the book “Quantitative Risk Management: Concepts, Techniques and Tools”, written by Prof. Paul Embrechts, Prof. Rüdiger Frey, Prof. Alexander J. McNeil and published in 2005 by Princeton University Press. We start by introducing a probabilistic framework for modelling financial risk, then we define the notion of risk factors for a portfolio of financial assets and we show the connection between risk factors and the terms of the Taylor expansion. Indeed, this representation is very useful and widely used by practitioners in risk management modelling. We also discuss the mapping of risks for equity, option and fixed income portfolios, including the relevant theory, proof of the main results and many solved exercises. Moreover, we study the main approaches for measuring risk and in particular, we concentrate our attention on Value-at-Risk and expected shortfall for Gaussian and t-distributed losses, proving the main formulas and solving many exercises. Finally, we present the variance-covariance method for measuring market risk and we show how it can be used in connection with factor models and principal component analysis to map risk-factor changes in real life situations. [more]

Thu. 23. Feb. 2006, 11.15-12.00, University of Zürich, 103/104, Plattenstrasse 14

Vidmantas Pleta:

     Quadratic Models in Credit Product Analysis: Theory and Implementation
Abstract: In this thesis we investigate quadratic models in credit risk related product pricing. The quadratic models were originally proposed by Ahn, Dittmar and Gallant (2002) and Leippold and Wu (2002) to model the term structure of interest rates. We provide pricing formulas for corporate-defaultable bond, single name credit default swap and the first-to-default swap in the framework of Reduced Form Approach of credit risk modelling. We also present the Kalman Filter-Maximum Likelihood methodology and show how it can be used to calibrate Reduced Form models. We implement the default free and defaultable quadratic term structure models and evaluate their performance by calibrating them to the Swiss market data. [more]

Thu. 23. Feb. 2006, 10.15-11.00, University of Zürich, 103/104, Plattenstrasse 14

Songtao Wang:

     The pricing of oil-linked contingent claims: a comparison of different models
Abstract: In the beginning, we analyze the future global oil demand and supply equilibrium and conclude that the oil supply will be able to satisfy the demand in a rather long period. However, the higher production cost will prompt the equilibrium price in the future. So, the mean reverting level of the spot prices of crude oil should be not in-variant or more precisely it should on average increase even though it will fluctuate from time to time. The pricing of oil-linked contingent claims critically depends on the assumed stochastic processes of the underlying assets. In this paper, we discuss about three main pricing models of oil-linked contingent claims: the factor models, the model based on the term structure of futures prices and the model which generalizes and combines the former two models. The factor models are currently most popular. For each of the factor models, the underlying factors are assumed to follow diffusion processes. One of the characteristics in our paper is that the interest rate is assumed to follow a square-root diffusion process such that it is always positive. When the interest rate follows a square-root diffusion process, the approach (by Bjerksund (1991)) which has been used to derive the closedform formulae for the prices of futures and futures options is not applicable any more. In this case, we apply the so-called affine model in order to obtain the closed-form solutions. In addition, when we consider a spot price process with stochastic volatility and jump diffusion, the characteristic function techniques which are first developed by Heston (1993) can be used to obtain the closed-form formulae for the prices of futures prices. The model of term structure of futures prices developed in this paper is originally inspired by the workings of Ho and Lee (1985), and Heath, Jarrow and Morton (1988) and it is imported into the pricing of commodity contingent claims. The advantage of this model is that it can fully make use of the information contained in the futures markets of crude oil. Within the framework of this model, the prices of the futures options are easy to obtain. In addition, more sophisticated financial derivatives of crude oil like swaps can be analytically priced in this framework, it is not practical to achieve this goal in the factor models. The simple one-dimensional term structure model is proven to be equivalent to the standard Gibson and Schwartz (1990) model. The generalized model in essence is a multi-factor model except that the continuously compounded forward interest rates and future (forward) convenience yields are assumed to follow the HJM (1992) processes. In this way, we can make use of the information not only in the futures markets but also in the bond markets. In this model, we get the closedform solutions for the prices of forward and futures options. Under certain assumptions, this model can be reduced into the factor model or the terms structure model, that is, it is a general extension of the former two models. This can be seen in the examples given in the end. Besides these models above, Routledge, Seppi, and Spatt (2000) and Pirrong (1998) have also tried to price the oil-linked contingent claims by using the equilibrium model in which the convenience yield is endogenously determined by the level of inventories, but not given exogenously as in the above models. The disadvantage of this approach is that the level of inventories is difficult to observe. Moreover, it is rather difficult to obtain a reasonable analytical formulae for the prices of oil-linked contingent claims like futures and futures options under the equilibrium model. [more]

Tue. 21. Feb. 2006, 14.45-15.30, University of Zürich, 103/104, Plattenstrasse 14

Donato De Feo:
     An Analysis of Hedge Funds Returns

Abstract: Hedge Funds outperform traditional markets. However this result is not definitive since some strategies show autocorrelation in their returns. Traditional practices of ranking investments is also analysed. Limitations of the Sharpe ratio are highlighted. By a procedure of numerical maximization, the paper shows that Sortino and Omega ratios are better tools for ranking investments in Hedge Funds. [more]

Tue. 21. Feb. 2006, 13.45-14.30, University of Zürich, 103/104, Plattenstrasse 14

Karin Soosova:
     A Predictive Model for Event Driven Hedge Fund Returns

Abstract: A major part of the growing literature on hedge funds focused on the study of risk and return characteristics compared to other asset classes, style analysis, several authors tried to find explanatory factors on a contemporareus basis. However, up to now there were few attempts to predict hedge fund returns. One of them is the paper by (Amenc et al., 2002), which relies on a linear prediction model for hedge fund index returns based on variables known to have explanatory power for other types of securities, mainly stocks. Indeed, evidence for predictability in stock returns was found by many authors, for example by (Keim et al., 1986), (Fama et al., 1989), (Ferson et al., 1993), (Lo et al., 1997), and (Avramov et al., 2005). Based on the paper by (Amenc et al., 2002), this thesis is dedicated to the prediction of event driven hedge fund returns. The reason why the focus is on this type of hedge funds is twofold. First the relative importance of event driven hedge funds in the hedge fund universe is growing. A good example of the growth dynamics is the period between 1990 and 2002, when the relative portion measured by assets under management increased from 2.4% to 4.7% for distressed strategies, from 0.6% to 2.03% for merger arbitrage strategies and from 3.84% to 12.15% for event driven strategies (see (Nicholas, 2004)). Moreover, according to the Deutsche Bank Alternative Investment Survey (Dyment et al., 2005) the event driven strategy belongs to strategies with the deepest market penetration besides long/short equity and multi-strategy. About 60% of all investors involved in the survey have exposure to the event driven style. Second, strategies under the common description event driven are often claimed to be cyclical, resp. their return to be strongly dependent on the state of the aggregate economy. If this would be true, and if the relationship of event driven hedge fund returns and the business cycle would be stable, one might be able to utilize this fact in prediction of event driven hedge fund returns. The rest of the thesis is organized as follows. Section 1 defines the event driven hedge fund style and its substyles and provides an overview about the relationship of their returns to the business cycle as described by other authors. Section 2 compares event driven hedge fund returns and growth of industrial production (as a proxy for GDP growth) as a basis for further analysis. Section 3 contains the main methods and results from (Amenc et al., 2002), which are relevant for this theses. Section 4 explains the methodology, Section 5 is dedicated to a short description of data and data sources, Section 6 presents main results and the last Section concludes. [more]

Tue. 21. Feb. 2006, 13.00-13.45, University of Zürich, 103/104, Plattenstrasse 14

Anna Georgieva:
     The Use of Structured Products: Applications, Benefits and Limitations for the Institutional Investor

Abstract: The institutional investor is in the business of understanding, pricing and managing risks to earn a return for the benefit of all stakeholders. In this paper I discuss how structured products can be used by institutional investors. In a perfect world (Arrow-Debreu state-claim framework) there exist enough securities to recreate any payoff. Some assumptions of this idealized world are: there exist basic securities, Arrow securities, that they have a risk-free payoff in any state, no transaction cost, no information asymmetry, all investors have the same expectations. Then derivatives are redundant instruments, as they can be replicated. The price of the replicating strategy should be equal to the price of the derivative; otherwise there is an arbitrage opportunity. Several research papers discuss the optimal existence of derivatives. [Merton 1971], [Carr Madan 2001], [Carr Madan 1998], [Liu Pan 2003], [Ross 1976]) The research results are usually dependant on assumptions about the process of the underlying. The case of including derivatives in an investor’s portfolio is usually solved making the assumption that investor preferences follow a certain mathematical function. The optimal investment in derivatives is then determined as the solution which maximizes the investor’s utility function. A closed form solution may or may not be available depending on the assumptions about the underlying process and the utility function. I treat the problem in a practical, applied way. Needless to say, financial markets have readily justified the existence of derivatives and derivatives related products. The focus is on how structured products can be handy to an institutional investor, as opposed to how do we price, replicate and hedge them. While in the back of every properly priced derivative there is a lot of mathematics, in this paper I focus on the investment interpretation and application. I present structured products as a natural investment choice of an institutional investor who faces the business constraints of a liability stream and of stakeholder and client expectations. Their main applications are in creating risk-return flexibility, isolating risks and providing exposure opportunities. I point at possible specific applications, but there is no almighty product that will magically solve all investment problems and unless a specific investor is consider it is impossible to make a strong statement about the best choice. For a retail institutional investor, structured products present new ways to reach the investment needs of clients by adding new products to the product basket, preserving the level of distribution fees and increasing the ability to raise new money. For the pension or trust fund investor, in particular in a core-satellite framework, structured products provide payoff flexibility, bundled or unbundled exposure to new and old asset classes, and can be optimally added as satellites to the investment portfolio. For the asset manager in an insurance company, structured products stand out with their ability to implement sophisticated investment views, and to isolate and hedge risks. Research on the pricing and replication of some of these structures are widely available; others do not have a closed-form solution. The most flexible approach is using Monte Carlo (MC) pricing tool Based on the martingale approach of derivatives pricing, this approach can price any possibly payoff and has gained widespread acceptance among practitioners. [more]

Tue. 21. Feb. 2006, 10.15-11.00, University of Zürich, 103/104, Plattenstrasse 14

Kartik Reddy:
     Real Option Valuation of Investment Decision in Indian Electricity Sector

Abstract: This paper is designed to study the effects of the new deregulation laws in the Indian Electricity Sector on new investment opportunities using the theory of Real Options. The main reason for using Real Option framework is that there are many embedded options which increase the value of investing which are missed by the normal DCF method. The paper is organized in the following way. Firstly the main features of the Electricity Act are mentioned, followed by the DCF analysis of invest- ment. This is extended by including the real option analysis by sim- ulating mean-reverting process and mean-reverting process with jump for electricity prices. Further more the paper develops theory for ex- tending the real option framework to include stochastic prices for both electricity prices and fuel prices. Also Schwartz model is discussed for simulating prices. Finally some results are discussed. [more]

Tue. 7. Feb. 2006, ETH Zürich, 11.15-12.00, HG F 26.5, Rämistr. 101

Kai Schnee:
     Dynamical systems and market instabilities

Abstract: We develop in this thesis a non-stochastic financial market model building on results by A. Corcos et al. and H. Föllmer et al. Our price process will eventually develop chaotic behavior and bubbles, which end in market crashes. The log-return distribution is shown to be non-normal and skewed with fatter tails. The market model considered, consists of agents who invest according to time dependent performance measures and forecasts, which build on three elementary trading strategies: the fundamentalist's, the chartist's and the behaviorist's trad- ing strategy. We do not introduce any bounds on the weights of these elementary trading strategies as is done in [2]. By incorporating all three trading strategies into an economically meaningful pricing mechanism, we are able to capture irrational as well as rational behavior in the market. [more]

Tue. 7. Feb. 2006, ETH Zürich, 10.15-11.00, HG E 22, Rämistr. 101

Georges Steinmann:
     Order Book Dynamics and Stochastic Liquidity in Risk-Management

Abstract: The core of this paper is to model the liquidity risk of a large investor. It is an empirical approach to real life data. We will restore the order book data from the Swiss Stock Exchange and deduce the liquidity of selected Swiss Market Index titles. We are going to try several approaches for modelling liquidity and mentioning their advantages and disadvantages. With our ¯nal method for modelling liquidity, we are going to simulate liquidity scenarios. Our application to risk management will be the dynamic delta hedge of a large trader. With the simulated liquidity, we will be able to calculate the corresponding liquidity risk. In an extension we incorporate stochastic volatility. Finally we will compare the liquidity exposure with those form Gamma and Vega risk. [more]

Mon. 6. Feb. 2006, ETH Zürich, 13.30-14.15, HG F 33.1, Rämistr. 101

Mihnea Constantinescu:
     Methodologies from Fixed-Income Markets for Pricing Energy Related Contracts

Abstract: The recent oil and gas price-outbursts and their repercussions throughout all sections of the economy emphasized once more the importance of hedging when the underlier is an energy-related asset. Besides this, the process of deregulation of energy markets added its share of instability in a sector with increasing competition and price volatility. The energy business has become more complex and riskier. The purpose of this work is to elaborate on the appropriate risk reduction and hedging techniques accomplished through the use of financial contracts. The pricing of these contracts is performed in a framework borrowed from fixed-income markets. The advantage of this model is that we by-pass traditional valuation problems caused by non-storability. [more]

Mon. 6. Feb. 2006, 10.15-11.00, University of Zürich, 103/104, Plattenstrasse 14

Eivind Helland:
     Valuation of Technology Investment Projects by the Real Options Approach
Abstract: In this work, the real option theory formed the basis of a tool developed to value a technology-based project and to provide information supporting management in making strategic decisions relating to this project in an actual company setting. Technology valuations assess the value of early stage technologies and are generally performed before undertaking risky investments. The goal was more specifically to provide a technology valuation tool suitable for multiperiod investment decisions. The real option analysis is considered to give a more accurate project value than the traditional net present value (NPV) approach. NPV can greatly undervalue potential projects, because it ignores the value of flexibility. Real options take into account and value the flexibility to expand, contract, extend or abandon projects in response to unforeseen events during the innovation phase. Indeed, managers often overrule NPV results, supporting projects with low or negative NPV; it is their intuition that takes the value of the flexibility of a project’s real options into account. From a financial and strategic point of view, the real option valuation method is used to optimise managers’ use of project choices in order to maximise the expected net present value by evaluating multiple project branches. In the presently evaluated case, the total net project value was identified to be dependent on both later decisions made by ABB’s business partner (denoted Partner Company), and on decisions made by ABB concerning a switch of production centres and/or project abandonment. It was determined that by selecting to enter a captive market with a low expected NPV, ABB would gain the possibility to sell their own standard products at a later stage, generating high profits. Additionally, the real option analysis showed that the project could generate large positive profits due to the option to shift production centre abroad during the project’s life span. The analysis showed a clear support for entering the new captive market. The real option approach proved to be a simple means used in a dynamic setting allowing a quantitative evaluation of an ongoing long-term project subject to a number of potential outcomes at different stages. [more]

Thu. 2. Feb. 2006, ETH Zürich, 11.15-12.00, HG G 26.3, Rämistr. 101

Rheia Khalaf:
     Replicating Portfolio for the BVG/LPP Minimum Interest Rate

Abstract: Several events, such as the crash in equity markets, the fall in bond yields and the increased longevity, have affected the financial stability of insurers. For these reasons and more, insurance companies have been looking for more accurate ways to value their liabilities, and to improve their asset liability management skills to better fulfil their obligations. One persisting issue in Switzerland is the unpredictable minimum interest rate that pension institutions must guarantee for the occupational pension plans subject to the BVG/LPP. The aim of this paper is to present this issue, the general framework and enough background information. Rules for determining the minimum rate are discussed, and replicating portfolios that guarantee some of these rules are defined. [more]

Wed. 18. Jan. 2006, 10.15-11.00, ETH Zürich, HG-F-26.3, Rämistr. 101
Gabriel Drimus:
     Quantitative Strategies for Correlation Trading

Abstract: Stochastic equity correlation is a widely observed feature in the financial markets. Moreover, recent work (Drissen et al) confirms that investors demand a (negative) premium for correlation risk. This has already been recognized in practice and correlation trading, also known as dispersion trading, has become a popular trading strategy. Despite its practical importance, correlation trading has received little, if any, academic treatment. Since it is a rather sophisticated trading strategy, the conventional approaches to correlation trading have been less than satisfactory. In the present thesis, we start from the theory of volatility trading (as developed, in particular, by Carr, Madan and Derman et al) and identify a number of quantitative strategies for correlation trading. In particular, we have sought to improve on the current practices to correlation/dispersion trading. Our trade designs vary according to whether we use variance swaps or portfolios of vanilla options as building blocks. A new payoff profile, hereafter named saddle, is introduced as an alternative to the conventional straddle and strangle as building block for correlation trades. Numerical simulations show that our trades are well designed to capture correlation.

Mon. 16. Jan. 2006, 16.15-17.00, ETH Zürich, HG-G-26.1, Rämistr. 101

Stefan Kruchen:
     Dividend Risk

Abstract: Common derivative pricing theory assumes that dividends are known. Comparing realized divi- dends with dividend forecasts, we ¯nd evidence for uncertainty about dividends. We investigate the impact of dividend uncertainty on European and American option prices. We discuss methods to extract information about dividend uncertainty contained in option prices. We find that the impact of dividend uncertainty on option prices is negligible. Since dividend risk depends on the quality of dividend forecasts, research on the latter is a promising task. We propose a modification of Lintner's (1956) partial adjustment model for dividends which improves prediction of dividend cuts. [more]

Mon. 16. Jan. 2006, 15.15-16.00, ETH Zürich, HG-G-26.1, Rämistr. 101

Annelis Lüscher:
     Synthetic CDO Pricing Using the Double Normal Inverse Gaussian Copula with Stochastic Factor Loadings

Abstract: Collateralized Debt Obligations (CDOs) are credit derivatives that have gained interest in recent years, both from the market side, because of a dramatic increase in traded contracts, as well as from an academic side because the pricing of such contracts is difficult and still an open issue. At a very simple level a collateralized debt obligation, is a transaction that transfers the credit risk of a reference portfolio of assets. The defining feature of a CDO structure is the tranching of credit risk. The risk of loss on the reference portfolio is divided into tranches of increasing seniority. Losses will first affect the 'equity' or ’first loss’ tranche, next the ’mezzanine’ tranches, and finally the ’senior’ tranches. In this thesis the pricing of tranches of synthetic CDOs is studied. In a synthetic CDO the reference portfolio consists of credit default swaps. Chapter 1 explains some basic aspects of CDOs, such as trading strategies, leverage, and CDO indices. The general approach to pricing a CDO tranche is introduced in Chapter 2. It shows that the CDO pricing problem is solved as soon as the loss distribution of the reference portfolio can be calculated. In Chapter 3 the Gauss copula model for loss distribution modelling is introduced. The Gauss copula model is the approach most often applied by practitioners. The large portfolio approximation is introduced as well. In Chapter 4 some issues arising by applying the Gauss copula model for CDO tranche pricing are discussed. This Chapter shows why a trader relying on the Gauss copula model should be very careful. Some extensions to the Gaussian copula model are reviewed in Chapter 5. In Chapter 6, CDO pricing using two extensions to the Gauss copula model, the double normal inverse Gaussian model (double NIG model) and the Gauss model with stochastic factor loadings, are explained in detail. Additionally, a new extension to the Gauss copula model is developed: the double normal inverse Gaussian model with stochastic factor loadings. In Chapter 7 the numerical results of pricing tranches of the DJ iTraxx with the four models introduced in Chapter 6 are compared. In summary, all the three tested extensions to the Gauss one factor model significantly improved the fit to market data. Even though the double normal inverse Gaussian model with stochastic factor loadings produced the best fit, for CDO pricing the simple double NIG model or the Gauss stochastic factor loadings model may be preferred by practitioners due to the greater numerical efficiency. [more]

Wed. 11. Jan. 2006, 18.15-19.00, University of Zürich, KOL-F-103, Rämistr. 71

Blaise Roduit:
     Fixed Income Performance Attribution - Analysis of a Multi-Currency Bond Portfolio

Abstract: The two key asset classes available to investment managers are equities and bonds. Equity attribution has been around for a while and well-established methods of attribution have been developed. It is therefore tempting to generalize these methods to fixed income attribution. However, in doing this the performance analyst ignores essential characteristics of fixed income investments. In many points, risk factors in fixed income investments are fundamentally different from those in equity. Some of them do not even have an equivalent in the equity attribution universe: these include yield curves and credit spreads. Furthermore, the effect of yield curve moves and spread changes on bond value is non-trivial. This paper proposes in the first part to review the different factor decompositions and methodologies used in the fixed income industry. A special emphasis is put on the yield curve shift effects (parallel, twist, butterfly, reshape) which play a central role in performance attribution. In the second part we discuss the practical problems of data quality that usually occur when implementing a fixed income performance attribution. Then we will run a Fixed Income Performance Attribution analysis (FIPA) on a real portfolio and interpret the results obtained. We finish by checking which FIPA factors are the main driver of excess returns and if excess returns identified are still present under a risk-adjusted basis. [more]

Thu. 22. Dec. 2005, 10.15-11.00, ETH Zürich, HG-G-26.3, Rämistr. 101

Robert Schöftner:
     Time-Varying Dependence Modelling of Market and Credit Risk

Abstract: In order to study the dynamic dependence structure between mar- ket and credit risk drivers, the VECM-DCC approach is proposed. This botton-up approach model for risk aggregation captures short run dynamics as well as long run equilibrium relationships between underlying risk factor time series. Furthermore, it incorporates time-varying conditional correlations between and heteroscedasticity of components. It is shown that the established model provides a good empirical fit verified by performance measurement. The model has many potential applications such as market and credit risk portfolio measurement. [more]

2. Cycle (2003/04)

Thu. 24. Mar. 2005, 11.15-12.00, ETH Zürich, HG-G-26.3, Rämistr. 101

Effi Shaked:
     Dynamic Risk Assessment Model for Long-tail Liabilities

Abstract: Existing methods employed for assessing and managing risk from liability contracts fail to incorporate information input during intermediate periods throughout the entire timeframe development of the contracts. Furthermore, static risk measurement techniques have shortcomings in expressing the true risk incorporated in these contracts. This paper will assess these risks using a different methodology, i.e. through modeling a single liability claims development process. This approach could permit assessment of both unconditional and conditional distributions of liability reserves during each given time period. Once aggregated into a liability portfolio, it would then be appropriate to apply dynamic risk measures to assess the incorporated risk from both an insurance and reinsurance perspective. [more]

Thu. 24. Mar. 2005, 10.15-11.00, ETH Zürich, HG-G-26.3, Rämistr. 101

Dr. Maximilian Seifert:
     About the Stochastic Volatility Model of Carr, Geman, Madan and Yor

Abstract: The mathematical framework of the stochastic volatility model of Carr, Madan, Geman and Yor is presented. Their construction relies on the assumption of the martingale marginal property. Carr et al. established this property for a special case when the rate of time change follows a Cox-Ingersoll-Ross process. We show that this property always holds when the rate of time change follows an Ornstein-Uhlenbeck process driven by a subordinator. [more]

Thu. 17. Mar. 2005, 11.15-12.00, Uni Zürich, SOC-U-1, Rämistr. 69

Maria Magdalena Soare:
    A Quantitative Approach for Stress-Testing the Term Structure

Abstract: Actual standardized stress testing scenarios for interest rates are based on historical realizations of interest rate changes and measure the impact of these shocks from the past on the actual portfolio value. We suggest in this paper a parameterized stress testing procedure for the term structure of interest rates. After identifying the factors driving the term structure we select the tail of the empirical distribution of each risk factor using state-of the-art approaches and model the probability distribution of these observations using Extreme-Value-Theory(EVT). Finally, we simulate extreme events in the risk factor and record the influence on the term structure. Our model can simulate various shapes of the term structure and we can approximate the impact of the stress event on portfolio values without performing expensive simulation procedures. Our approach is quite general. It can be performed for different types of term structures like the zero curve, the yield-to-maturity curve, the par curve, or the swap curve. [more]

Mon. 7. Mar. 2005, 10.15-11.00, ETH Zürich, HG-D-5.1, Rämistr. 101

Ousmane Kaba:
     Saddlepoint Approximations for Portfolio Credit Risk Modelling

Abstract: TBA [more]

Fri. 18. Feb. 2005, 14.15-15.00, ETH Zürich, HG-D-5.1, Rämistr. 101

Giuliana Bordigoni:
     Robust Utility Maximization with an Entropic Penalty Term: Stochastic control and BSDE methods

Abstract: This work studies a robust control problem that consists in minimizing over a suitable class of probability measures (scenarios) a felicity process plus a penalty factor. First we extend results by Skiadas and Lazrak-Quenez to include a terminal utility. Then we tackle the robust control problem using a stochastic control approach. In particular, we provide a proof for the existence of a solution and find explicitly the minimizer. Finally we maximize over consumption the functional obtained by the minimization by applying stochastic control techniques and exploiting known results. [more]

Fri. 18. Feb. 2005, 9.15-10.00, Uni Zürich, PLM 103/104, Plattenstr. 14
Patrick Bolliger:
     Stochastic lifestyling in the presence of mean-reverting stock prices

Abstract: The focus of this study is to find and analyze optimal asset allocation strategies for a pension plan member. The plan member pays a constant fraction of his salary into the pension plan. The objective is to optimize her expected terminal utility. The pension fund can be invested into a risk free asset and a risky asset. For the risky asset we assume mean-reverting market price of risk, which can be interpreted as business cycles of the underlying economy. To get analytical results it is necessary to hedge future salary streams which leads to a complete market setting. Pension fund manager widely use a strategy called deterministic lifestyling. We show that this strategy is suboptimal. We derive the optimal strategy called stochastic lifestyling. This strategy is easy implementable and presents a massive improvement over usually used strategies, especially for less risk averse plan members. [more]

Tue. 8. Feb. 2005, 11.15-12.00, Uni Zürich, PLM 103/104, Plattenstr. 14

James Taylor:
     Review of Option Pricing under Stochastic Volatility and Lévy Processes

Abstract: This thesis traces the development of alternative option pricing models to that proposed by Black and Scholes in 1973. It reviews a selection of these from Robert Merton's Jump diffusion in 1976 to the models of stochastic volatility applied to Lévy processes proposed by Carr, Geman, Madan, and Yor in 2003. It is not encyclopedic in its coverage of the ver y many available model but seeks to describe a logical progression of them. Wherever possible the improvements that a particular model offers over the others are highlighted and the practical applicability tested. [more]

Fri. 4. Feb. 2005, 16.15-17.00, ETH Zürich, NW-B-81, Clausiusstr. 25

Sujatha Prakash:
     On the use of high dimensional Quasi Random Sequences for risk measurement

Abstract: Risk modeling often goes to using models which have no closed form solutions. In such cases, it is common to use Monte Carlo (MC) techniques. Efficiency of Monte Carlo methods can be improved by using variance reduction techniques or with alternate methods like the Quasi Monte Carlo (QMC). The difference between QMC and MC techniques is that the former uses quasi random or low discrepancy sequences; where as MC uses random sequences. Several methods for producing low discrepancy sequences have been proposed by Halton, Sobol, Faure and Neiderreiter. Though each of these algorithms produce low discrepancy sequences in high dimensions, not all these behave reliably when one extends to high dimensions [3]. Even if these sequences exhibit good asymptotic behavior in high dimensions, it does not imply that they will necessarily perform well in practical applications. In this thesis, the approach of using Sobol sequences to risk measurement is investigated. More specifically, we will
*State formal theoretical properties a good Sobol sequence ought to possess.
*Implement a Sobol sequence generator in high dimensions
*Investigate the effect of applying the sequence to risk measures and allocation issues in the context of a
- Simple model for aggregation
- Simple credit risk model
*Lastly we touch on the issues in application of quasi random sequences. [more]

Fri. 4. Feb. 2005, 15.15-16.00, ETH Zürich, NW-B-81, Clausiusstr. 25

Marco Tolotti:
     Credit risk under incomplete accounting information: A discretized approach in filtering language

Abstract: Relying on the paper of Duffie and Lando "Term structures of credit spreads with incomplete accounting information", based on information asymmetry in credit risk, we propose a discretized approach under filtering language. We model the logarithm (Z) of the firm asset value process V as a Markov chain. The debtholders do not have perfect information on the actual value of the firm; they receive only a discrete noisy stream of reports (Y). We study the pair (V,Y) as a discrete filtering system. Then, letting the increments go to zero, we compute the intensity of the default time. We compare our result with the result of Duffie and Lando in the brownian case. [more]

Fri. 4. Feb. 2005, 14.15-15.00, ETH Zürich, NW-B-81, Clausiusstr. 25

Alexis Bailly:
     Cost of Capital and Surrender Options for Guaranteed Return Life Insurance Contracts

Abstract: The opacity of traditional accounting systems for insurance companies is well known. This was confirmed recently by unexpected repercussions of stock market and interest rates movements on the financial strengh of many insurance companies. To improve transparency, new valuation standards are initiated by regulators or by professional bodies such as actuaries or accountants. Whether the purpose is pricing or risk management, the new standards are all based on a market consistent framework where assets and liabilities are valued at market value. Traditionnally the pricing and the risk capital assessement are treated separetely. In this thesis we build a unifying valuation framework where these two components can not be dissociated. To reflect the incompleteness of insurance markets and the limited access to equity capital, we introduce the notion of cost of capital. We analyse the impact of the cost of capital on the valuation of life insurance contracts with guarantees. In the last part of this thesis we focus on surrender options that represent today the most obscur risk for life insurers. We present models where the pricing can be precisely performed, but we also discuss certain aspects of policyholders behaviour. [more]

Thu. 3. Feb. 2005, 15.15-16.00, ETH Zürich, HG-E33.3, Rämistr. 101

Fabian Simond:
     Credit Risk Stress-Testing: The Case of a Real Estate Crisis

Abstract: In most OCDE countries, banks incurred big credit losses in the aftermath of the previous real estate market crashes. This took place in the context of the sharp economic downturn of the early nineties. In some countries, the business cycle was even driven by the real estate cycle. The latter was exacerbated by investor speculative behaviour and commercial banks generous lending policies. Considering the big proportion of loans collateralized by real estate, it is important for commercial banks to understand the dynamics of real estate markets when monitoring their credit portfolios. Their qualitative credit risk management is usually complemented by the estimation of the credit loss distribution under adverse real estate conditions. With a real estate stress-test, banks try to assess how much they would loose if a real estate crisis happened again. The original contribution of this paper is to present a new methodology for credit risk stress-testing based on a credit portfolio model. After an overview of the real estate markets dynamics, we analyse the credit portfolio sensitivity to real estate prices .Then, by using a generic credit portfolio model and a synthetic loan portfolio, we discuss the concept of risk concentration. Finally, our stress-testing approach is described using the generic model and compared to the standard approach by estimating stress loss distributions for the synthetic portfolio. [more]

Fri. 21. Jan 2005, 14.15-15.00, ETH Zürich, ML-E-13, Sonnegstr. 3

Beat Huggler:
     Modelling Hedge Fund Returns

Abstract: The principal aim of this paper is the modelling of hedge fund portfolios using representative proxies. Two competitive models are investigated in this paper: one using manager proxies, a so called Manager-Up model, and the second based on strategy proxies, a so called Style-Up model. These proxies are constructed using publicly available hedge fund return series. The serial dependence observed in the proxies is described by a multivariate AR-GARCH model. There is strong empirical evidence that the marginal distributions of the model’s innovations are skewed and heavy tailed, and hence we propose the use of a skewed-t distribution for their modelling. Under the assumption that no cross-lag correlation exists between the proxies, the cross-sectional dependence structure is only apparent in the innovations. Although there exists evidence of an asymmetric dependence structure between some of the proxies, a grouped-t copula is proposed to model the cross-sectional dependence structure of the innovations. Finally, the calibrated model is used to simulate hedge fund portfolio return series, which then are compared with similar portfolios constructed from the data. Keywords: hedge funds, portfolio simulation, ARMA-GARCH process, skewed-t distribution, asymmetric dependence structure, grouped-t copula. [more]

Thu. 20. Jan. 2005, 10.15-11.00, ETH Zürich, HG-E-33.3, Rämistr. 101

Saverio Massi Benedetti:
     Hedge Fund portfolio Selection with Higher Moments

Abstract: We start describing the hedge fund environment with emphasis on the analysis of the different managing styles and on how the distribution of the fund returns are affected by the strategy adopted. The class of Skew elliptical distributions proposed by Sahu et al. (2003) is defined together with the Skew Normal and Skew t special cases. Then the Bayesian inference technique is explained and specification of the models for Bayesian estimation is provided. A whole section addresses the estimation of the predictive distribution in order to take into account for parameter uncertainty and estimation risk. In the last section the empirical results obtained from the application of the proposed models to a dataset consisting of hedge fund strategies returns are presented. A preliminary assessment of the non-normality of hedge fund returns is also provided. [more]

Wed. 19. Jan. 2005, 10.15-11.00, Uni Zürich, KOL-G-212

Markus Thöny:
     Estimation Risk in Mean Variance: Portfolio Selection

Abstract: Finance theory generally assumes, that the investors know the distributional form of future returns. In practice, however, empirical evidence seems to suggest the opposite. This paper approaches portfolio selection in a Bayesian framework that allows to incorporate uncertainty about the parameters of the perceived return distribution (parameter uncertainty) as well as uncertainty about the type of the return distribution (distribution uncertainty). The two different levels of uncertainty are addressed by using an infinite Gaussian mixture model in which the mixing distribution is treated as the critical factor: If the mixing distribution is assumed to have a fixed parametric form, we are in the realm of parameter uncertainty. Contrary, if the mixing distribution is chosen to be random and modeled by a Dirichlet process, we are able to analyze decisions under distribution uncertainty. Both approaches are applied to a Swiss bond portfolio. The bond market is in general characterized trough highly correlated assets. Therefore, the known sensitivity of classical optimization procedures on the expected return forecast might be even more pronounced, and the bond portfolios constructed using sample estimates for the parameters of the return distribution are anticipated to be less diversified. In contrast, accounting for parameter and distribution uncertainty is expected to result in more diversified portfolios. To gauge the impact on optimal portfolio holdings, we compare the relevant allocations under parameter and distribution uncertainty with classical mean variance optimized portfolios. Depending on the investor’s relative risk aversion we found that accounting for parameter uncertainty leads to more balanced and, in terms of the certainty-equivalent loss, economical significantly different portfolios. Compared to investors facing parameter uncertainty, the investors accounting for distribution uncertainty are shown to allocate their money in clearly less diversified portfolios. [more]

Mon. 10. Jan. 2005, 16.15-17.00, ETH Zürich, ML-F-40, Sonnegstr. 3

Stefan Denzler:
    From Default Probabilities to Credit Spreads: Can Credit Risk Models Explain Market Prices?

Abstract: Default probabilities and credit spreads are important quantities to the credit markets. Perceived changes in the probability of default may forecast credit rating migrations to other rating levels or to default. Such changes in default probabilities have an effect on a company’s bond returns and credit spreads. In this thesis we develop and establish a model that quantitatively links actual default probabilities with risk-neutral default probabilities and credit spreads. The main input quantities to this study are merely industry yield data of different time to maturity and expected default frequencies (EDFs) of Moody’s KMV. The model adjusts actual default probabilities, proxied by EDFs by a functional relationship and some function of time to maturity to arrive at credit spreads (market prices). The proposed modeling approach is tractable, it provides a closed-form solution and it allows for suitable empirical testing. The model is empirically analyzed at an industry level approximating risk-neutral default probabilities and credit spreads from EDFs. The quality and reliability of the model is assessed by an out-of-sample analysis and by empirical tests on foreign bond markets as well as on the corporate level. The outcomes of the proposed model are additionally supported and verified by an independent Monte Carlo simulation study. The empirical results of this thesis clearly indicate that the suggested relationship enables to accurately approximate annualized risk-neutral default probabilities and credit spreads (market prices) from EDFs, independent of the time to maturity and the industry sector under consideration. Moreover, the testing methodologies suggest that the model is reasonably effective in an out-of-sample setting. Finally, the model produces consistent results on the European bond market and can be adequately used to approximate credit spreads and annualized risk-neutral default probabilities on the corporate level.

1. Cycle (2002/03)

Friday, 21. May 2004, 9.15-10.00, Uni Zürich, PLM 103/104

Henric Talborn:
     A Case Study: Trading in the Net Asset Value Discount for Investor

Abstract: In this case study I will present a hedge strategy designed for Investor, the largest holding company on the Swedish stock exchange and in the Nordic region. The strategy implies trading in the net asset value discount. The returns are uncorrelated with market index implying no priced market risk. Transaction costs and specific risk are considered and loss absorbing capital allocated. The strategy yields a statistical arbitrage profit when bid/ask spreads are ignored. However, when bid/ask spreads are considered the conclusion becomes unclear and there seems to be only small indications of arbitrage profit left. [more]

Tuesday, 20. Apr. 2004, 17.15-18.00, ETH Zürich, HG F 33.5

Lionel Sanchez:
     Pricing Basket of credit derivatives and CDO in factor models framework

Abstract: We consider a factor approach for the pricing of credit derivatives basket and synthetic CDO tranches for given default probabilities of obligors. Our goal is to deal in a convenient way with dependent defaults for a large number of names. We provide semi-explicit expressions for small number of names and apply the FFT(fast fourier transform) technique for the pricing of large names credit derivatives basket. We also compare prices under Gaussian and Clayton copulas and price CDO according to risk payments conventions. [more]

Tuesday, 13. April 2004, 17.15-18.00, Uni Zürich, RAK-E-6

Anca Antonov:
     Performance of Modern Techniques for Rating Model Design

Abstract: The usual qualitative assessment of individual risk of borrowers, other than individuals, relies on ratings. Due to the current emphasis on extensive data on individual borrower's risks, modeling became attractive for assessing risk in a comprehensive and objective manner, and for complying with the New Accord recommendation. There are several generations of models of credit risk and default probabilities, starting with the early statistical models linking ratings to financial characteristic of the firms, up to elaborate econometric technique, neural network models or based on Merton's model. The scope is to test the efficiency and the accuracy of statistical approach: logistic regression, discriminant linear and quadratic analysis, polynomial regression, k-nearest neighbors, Parzen window density comparing with different types of neuronal networks(multilayer perceptons, radial basis, learning vector quantization, or self organized maps). It emphasis on finding the most appropriate measure for the generalization performance (on the never seen data), as well as the link between the classical statistical models and neural networks. [more]

Tuesday, 13. April 2004, 16.15-17.00, Uni Zürich, RAK-E-6

Riccardo Gusso:
     An Application of EM Algorithm to Calibration of Dependent Credit Risk Models

Abstract: The object of this thesis is the analysis of two models for the joint probability of defaults of dependent credit risks, models that are based on a generalisation of the P´olya urn scheme. In particular we focus our attention on the problems related to the maximum likelihood estimation of the parameters involved, and to this purpose we introduce an approach based on the utilisation of the Expectation-Maximization algorithm. We show how to implement it in this situation and then analyse the results obtained, comparing them with results obtained by other approaches. [more]

Wednesday, 25. Feb. 2004, 15.00-16.00, ETH Zürich, HG F 33.5

Mingying Zhang:
     Regulatory Capital Requirements for Credit Risk under the IRB Approach in the Basel New Capital Accord - An empirical study of industry solution -

Abstract: This paper is an attempt to evaluate technology vendors’ solution of the Internal Ratings Based approach for capital adequacy determination within Basel II framework. In particular, it focuses on how SAS Basel II solution is structured with respect to the regulatory capital requirements; the results suggest that SAS Basel II solution not only provides high classification accuracy, but also proves to be an explanatory system.
The paper further addresses two IRB-related methodological questions. First, how can the probability of default be estimated using various statistical techniques, secondly, which potential issues will impact Basel Regulatory Capital Requirements calculation? We conclude that methods to estimate PDs and number of rating classes selected may lead to different IRB capital charges.
Finally, we compare different vendor solutions based on techniques offered. The results show that these solutions are similar products in terms of characteristic, but their market positions as well as reputation play also crucial roles.

Tuesday, 17. Feb. 2004, 15.00-16.00, ETH Zürich, HG F 33.1

Adam Czub:
     Statistical Methods of Valuation and Risk Assessment: Empirical Analysis of Equity Markets and Hedge Fund Strategies

Abstract: The purpose of this paper is first to describe a web-based tool that returns the different Value-at-Risk and related measures of risk (expected shortfall, volatility) for major equity market indices using standard methods as well as the most recent state-of-the-art methods. This internet tool continually backtests its own performance against the latest data. We describe the risk measures calculated by Riskometer on September 24, 2003 and January 9, 2004. In the second part of the paper, we analyse hedge fund strategies over a six years sample period using the database of indices compiled by Morgan Stanley Capital International. For a better understanding about dependence structures in hedge fund strategies we focus on analysing their bivariate distributions using Archimedean copulas. To identify style exposures to relevant risk factors we conduct a return-based style analysis of hedge fund strategies by relaxing the constraints of the Sharpe’s style analysis, and examine the significance of the style weights. Finally, we compare these results with those obtained by applying the Kalman filter and smoother technique. [more]

Tuesday, 10. Feb. 2004, 16.30-17.30, Uni Zürich, KOL-G-220

Boris Papa:
     Stock market volatility: A puzzle?
An investigation into the causes and consequences of asymmetric volatility

Abstract: One of the many stylised facts of stock market returns is the empirical finding that volatility is much higher when the market declines than when it rises. Conversely, the returns are low with the occurrence of high volatility and high with low volatility. This is an apparent contradiction that standard financial, consumer-based models cannot explain. We should identify this contradiction as a puzzle in keeping with traditional financial economics. This puzzle, like the others that have been discovered in the last twenty years, is the result of a weakness in the models and/or the data that was used. Does it involve issues of investor risk preferences, beliefs, and rationality assumption implicit in the models? Twenty years of experimental and empirical research has demonstrated that markets are not as efficient as one might assume. Investors are not as rational and risk preferences are stochastic. In addition to this, Prospect Theory criticised the standard expected utility hypothesis used to describe utility and investor performance preferences. Kahneman and Tversky propose a new framework to model the utility and risk preferences of investors. This new "value function" is concave for gains and convex for losses, which implies loss aversion of agents as the primary feature. This new preferences structure has been tested and verified in many experiments. Subsequently, new models have been developed combining Prospect Theory and classical finance, which seem to offer a better explanation of the characteristics of returns and risks in the stock market, leading to a solution of the many empirical puzzles. [more]

Thursday, 5. Feb. 2004, 16.00-17.00, Uni Zürich, KOL-G-204

Cornelia Glavan:
     An Application of Alternative Risk Measures to Trading Portfolios

Abstract: This study covers the advantages of expected shortfall as an alternative risk measure to value-at-risk and the results of implementing in practice the tools of extreme value theory. EVT is applied to a varied sample of trading portfolios across different sectors and sensitive to one and multiple risk factors. A detailed analysis of the tail of the profit & loss empirical distribution is performed with an emphasis on the estimates of value-at-risk and expected shortfall. The concept of expected shortfall is also used as a measure of sensitivity of the portfolio to risk factors, thus allowing to determine the main drivers of risk. Being involved with the market directly and on a daily basis, as well as considering the recent events in the Russian market - more specifically, the Yukos case, provided the opportunity to observe a real example when historical VaR fails to be coherent. [more]

Thursday, 5. Feb. 2004, 15.00-16.00, Uni Zürich, KOL-G-204

Dr. Hansjörg Furrer:
     The Term Structure of Interest Rates as a Random Field. Applications to Credit Risk

Abstract: The principal aim of this paper is the modeling of the term structure of interest rates as a positive-valued random field. Special emphasis is given to chi-squared fields which can be generated from a finite number of Gaussian fields. In particular, we introduce a short rate model which is based on the square of an Ornstein-Uhlenbeck process. It is shown that bond prices can be expressed as an exponential-affine function of the short rate. We extend our approach to the credit risk area and model the default intensities of a class of obligors as a two-parameter positive-valued random field. Finally, random fields will be applied to the modeling of firm values in a structural credit risk framework. [more]

Tuesday, 3. Feb. 2004, 13.00-14.00, ETH Zürich, ML E 13

Gorazd Brumen:
    Deterministic Solution of American style Optimal Stopping Problems with Levy Driven Underlyings by the Penalty Method

Abstract: The solutions of American optimal stopping problems with price process being a jump-diffusion or a general Lévy process satisfy parabolic integro-differential inequalities. We address here the numerical solution of these problems for the CGMY processes by the penalty method and investigate its convergence properties. [more]

Monday, 2. Feb. 2004, 10.00-11.00, Uni Zürich, KO2-F-172

Andrea Girometti:
    Entry and Exit Decisions Problem: A Survey

Abstract: In this survey, the entry-exit decisions problem is studied. The problem concerns to the investment and disinvestment decisions process of a .rm, when its output price is stochastic. Typically, this is the problem faced by an oil company or by a .rm involved in the commodities markets. The .rst approach, here analyzed in detail, was proposed by Dixit in 1989 and it is based on the contingent claim theory. In particular, the values of a .rm in both activity and inactivity states are determined by using the theory of real options pricing. Thanks to the so-called value-matching and smooth-pasting conditions, it is possible to interlink these two .rm’s values and, therefore, to determine a pair of trigger prices, giving an optimal decision policy. The optimal policy .xes the levels of the output prices at which it is economically convenient either to start the production or to abandon the market. In addition, some interesting extensions of the basic model are presented and, .nally, the two most recent approaches are explained. The .rst one is based on the ”mark-up” concept, the second one is based on the optimal stopping time theory. [more]

Friday, 30. Jan. 2004, 9.00-10.00, ETH Zürich, HG F 26.5

Enrique Marrufo-Garcia:
    Modelling Issuer-Specific Risk for Non-Government Bonds

Abstract: The following paper describes the approach used to calculate Issuer-Specific Value at Risk (VaR) and Expected Shortfall (ES) for Non Government Bonds. This approach combines Historical Simulation Value at Risk (HSVaR) with Monte Carlo simulation. Although the calculations presented here estimate bond price risk for a bond Issuer, they are not used on historical price of that bond but solely on its Yield To Maturity (YTM) and Time to Maturity (TTM). Plausible changes in Issuer Spread are derived from historical movements in the spread of Rating specific universes in the bond’s currency and at its TTM. As the first step in the process, this characterisation will be referred to any Issuer with a given YTM and TTM. As a consequence two different Issuers with the same values will have exactly the same estimated risk and, at a Portfolio level, no diversification effect will be attained. To build a more robust solution, whose results are more akin to empirically observed behaviour of actual bond portfolios, Monte Carlo simulation based on the innovations ’ distribution obtained from a GARCH(p,q) model is then performed. As a second step, the simulated paths for these two bonds (with identical TTM and YTM) will be highly, but not perfectly, correlated and diversification is rewarded. The approach implemented has not been found or discussed in the literature consulted. The solution herein explained is the result of several discussions and considerations worked together with Nicholas MacCabe from Julius Baer’s Group Risk Management Department. [more]
Keywords: Issuer-Specific Risk, Rating category, Risk measures, Discriminant Analysis, GARCH models, Fixed Income.

Friday, 19. Dec. 2003, 14.00-15.00, ETH Zürich, HG F 26.2

David Ardia:
    Analysis of Dependencies in Low Frequency Financial Data Sets

Abstract: This empirical study proposes a dependency analysis of monthly financial time series. We use the overlapping technique and non-parametric correlation in order to increase both accuracy and consistency. Copulas are used to test extreme co-movements between financial securities. Our results indicate that even in a low-frequency framework, the common practice of assuming independence over time should be taken with caution due to the presence of GARCH effects. In addition, extreme co-movements are observed across securities, especially for interest rates. [more]

Thursday, 4. Dec. 2003, 15.00-16.00, ETH Zürich, CLA J1

Julien Dinh:
     30 Years Fixed Rate Mortage Backed Securities Valuation

Abstract: Securitisation in its present form has been originated in the mortgage markets in the United States. It has been actively supported by the government to increase liquidity for mortgage finance companies. This secondary mortgage market has dramatically grown during the last two decades and surpasses now the size of the U.S. Treasury market. Despite the importance of these markets, the theory of mortgage valuation still represent an ongoing challenge to researcher. A lot of efforts have been made to understand the relevant factors driving their value, but the prepayment option make mortgage related securities difficult to price. [more]

Thursday, 27. Nov. 2003, 14.00-15.00, ETH Zürich, ETZ E40

Quan Gan:
    Modelling the Return Distributions of Multivariate Intra-day FX Series:
A Comparative Study

Abstract: In this thesis, multivariate series of high-frequency FX spot data for major FX market are investigated. First, I analyze in detail dependence structure as a function of the time scale. Particular emphasis is put on the tail behavior, which is investigated by means of copulas. Second, I fit various multivariate GARCH models for various frequencies. [more]

[RiskLab] [ETH Finance Group] [Swiss Banking Institute] [MAS Finance] [NCCR-FINRISK] [CCFZ]

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Last modified: Mon Oct 15 17:09:55 CEST 2007

Created and supported by Prof. Dr. Uwe Schmock until October 6, 2003. Design Michael Volkart. Content PD Dr. Erich Walter Farkas.