Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

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DMV Tagung 2011 - Köln, 19. - 22. September Donnerstag, 22. September Seminargebäude, S24 14:00 Kees Oosterlee (Delft) Efficient valuation methods for contracts in finance and insurance 14:40 Jan H. Maruhn (UniCredit, München) Exploiting GPUs and Adjoints for Rapid Monte Carlo Calibrations 15:20 Pascal Heider (Köln) Arbitrage-free Approximation of Call Price Surfaces 16:00h – 16:30h Pause 16:30 Ralf Korn (Kaiserslautern) Recent Advances in Option Pricing with Binomial Trees 17:10 Christoph Winter (Zürich) Wavelet Galerkin schemes for option pricing in multidimenstional Lévy models 17:50 Christian Jonen (Köln) Valuing High-Dimensional American-Style Derivatives: A Robust Regression Monte Carlo Method 178
DMV Tagung 2011 - Köln, 19. - 22. September Pascal Heider Universität Köln Arbitrage-free Approximation of Call Price Surfaces In this talk I present a construction of arbitrage-free call price surfaces from observed market data by locally constrained least squares approximations. Derivatives of the surface are computed accurately so that implied volatility, local volatility and transition probability density are obtained at no additional costs. Observed input data are afflicted by a price uncertainty and cause an input data risk on the computed call surface. I present a simple model for the input risk and perform an analysis to study and measure the effect of the input risk on the surfaces. With this analysis one can determine the trust-worthiness of the computed results and their implications on option pricing a posteriori. Christian Jonen Universität zu Köln Valuing High-Dimensional American-Style Derivatives: A Robust Regression Monte Carlo Method Pricing high-dimensional American-style derivatives is still a challenging task, as the complexity of numerical methods for solving the underlying mathematical problem rapidly grows with the number of uncertain factors. In this paper we extend the important class of regression-based Monte Carlo methods for valuing these complex financial products. The key idea of our proposed approach is to fit the continuation value at every exercise date by robust regression rather than by ordinary least squares. By using robust regression, we are able to get a more accurate approximation of the continuation value due to taking outliers in the cross-sectional data into account. In order to guarantee an efficient implementation of our Robust Regression Monte Carlo (RRM) method, we suggest a new Newton-Raphson-based solver for robust regression with very good numerical properties. We use techniques of the statistical learning theory to prove the convergence of our RRM estimator. In order to test the numerical efficiency of our proposed method, we price Bermudan options on up to thirty assets. It turns out that our RRM approach shows a remarkable convergence behavior; we get speed-up factors of up to over four compared with the state-of-the-art Least Squares Monte Carlo method proposed by Longstaff and Schwartz (2001). Literatur C. Jonen (2011). Valuing high-dimensional American-style derivatives: a robust regression Monte Carlo method. To be submitted. F. Longstaff and E. Schwartz (2001). Valuing American options by simulation: a simple least-squares approach. Review of Financial Studies, 14, 113 - 147. 179
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Frank Kutzschebauch Universität Be
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Ulrich Derenthal Ludwig-Maximilians
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Anna Dall’Acqua Otto-von-Guericke
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Eleutherius Symeonidis Katholische
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Felix Schlenk Universität Neuchât
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Edgar Brunner Universität Götting
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Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

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