PRisMa 2008

Prof. Dr. Uwe Schmock
(FAM @ TU Wien)
Welcome

Prof. Dr. Damir Filipovic
(Vienna Institute of Finance)
CDO Term Structure Modeling

Abstract: This work provides a unifying approach for valuing contingent claims on a portfolio of credits, such as collateralized debt obligations (CDOs). We introduce the defaultable (T,x)-bonds, which pay one if the aggregated loss process in the underlying pool of the CDO has not exceeded x at maturity T, and zero else. Necessary and sufficient conditions on the stochastic term structure movements for the absence of arbitrage are given. Background market risk as well as feedback contagion effects of the loss process are taken into account. Moreover, we show that any exogenous specification of the volatility and contagion parameters actually yields a unique consistent loss process and thus an arbitrage-free family of (T,x)-bond prices. For the sake of analytical and computational efficiency we then develop a tractable class of doubly stochastic affine term structure models.

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Dr. Antonis Papapantoleon
(FAM @ TU Wien)
Strong Taylor Approximation of SDEs and Application to the Lévy LIBOR Model

Abstract: The aim of this work is to provide a fast and accurate approximation scheme for the Monte-Carlo pricing of derivatives in the Lévy LIBOR model. The scheme is based on the strong Taylor approximation of the random terms entering the drift of the successive LIBOR rates; it offers a tractable alternative to "freezing the drift" at an accuracy similar to the full numerical solution. Numerical illustrations will also be presented.
(This talk is based on joint work with Maria Siopacha and Friedrich Hubalek.)

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Dr. Friedrich Hubalek
(FAM @ TU Wien)
On Trades, Volume, and the Martingale Estimating Function Approach for Stochastic Volatility Models with Jumps

Abstract: We introduce a variant of the Barndorff-Nielsen and Shephard stochastic volatility model, where the non-Gaussian Ornstein-Uhlenbeck process describes trading volume or the number of trades instead of unobservable volatility. We develop an explicit estimator using martingale estimating functions and analyze its asymptotic behaviour, when observations are made on a fixed grid with the horizon tending to infinity.
(based on joint work with Petra Posedel)

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Dr. Stefan Gerhold
(PRisMa Lab, FAM @ TU Wien)
Lévy-Sheffer Systems and the Longstaff-Schwartz Algorithm for American Option Pricing

Abstract: The Longstaff-Schwartz Algorithm has become the method of choice for pricing American derivative contracts in high-dimensional settings. It approximates value functions by regression on a prescribed set of basis functions. If the number of basis functions is increased, the number of Monte Carlo paths must grow, too, to ensure convergence. Glasserman and Yu (Ann. Appl. Prob. 2004) have quantified the relation between these two parameters in the case where the underlying process is (geometric) Brownian motion. We extend this analysis to several well-known Lévy processes, using martingale identities found by Schoutens.

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Dipl.-Math. Verena Goldammer
(PRisMa Lab, FAM @ TU Wien)
Modeling and Estimation of Dependent Credit Rating Transitions

Abstract: Simultaneous defaults in large portfolios of credit derivatives can induce huge losses. To take this into consideration, we apply an interacting particle system to model the credit rating transitions of firms. In our model the credit rating changes of the firms follow a homogeneous Markov jump process with the generator of the strongly coupled random walk process introduced by Spitzer (1981). The model depends on two sets of parameters, the vector of dependence parameters and the generator of the rating transitions of a single firm. For these parameters the maximum likelihood estimators are computed using historical rating transitions and sojourn times. Simulation of the process shows, how the shape of the profit and loss distribution of a large portfolio of defaultable zero-coupon bonds is influenced by the dependence vector.

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Dr. Stefan Tappe
(Vienna Institute of Finance)
Bilateral Gamma Processes in Finance

Abstract: In recent years more realistic stochastic models for price movements in financial markets have been developed by replacing the classical Brownian motion by Lévy processes. We propose a new family of Lévy processes: Bilateral gamma processes. In this talk, we present the properties of these processes and their generating distributions, and show how they are related to other distributions considered in the literature. Afterwards, we apply bilateral gamma processes for modelling financial market fluctuations.

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Dr. Miklos Rasonyi
(Hungarian Academy)
Modelling Markets with Transaction Costs

Abstract: We present a survey of market models with proportional transaction costs in continuous time. Various concepts of arbitrage and their relationship to price systems are discussed. Recent research has shown that in the presence of transaction costs one gets a considerably larger class of admissible market models (including e.g. fractional Brownian motion-based models) and that absence of arbitrage depends on "coarser" properties of the price process than in the frictionless case. We shall discuss these issues in comparison with what happens in illiquid markets or in frictionless markets under restrictions on the set of trading strategies.

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