Past Mathematical Finance Seminar

3 June 2005
14:15
Abstract
We propose a model for credit risk with endogenous default and jump risk. The model has four attractive features. <ol> <li>It can generate flexible credit spread curves. </li> <li>It leads to flexible implied volatility curves, thus providing a link between credit spread and implied volatility. </li> <li>It implies that high tech firms tend to have very little debts. </li> <li>It yields analytical solutions for debt and equity values. </li> </ol> This is a joint work with Nan Chen (a Ph.D. student at Columbia University).
  • Mathematical Finance Seminar
20 May 2005
14:15
Kees Oosterlee
Abstract
In this talk, we present several numerical issues, that we currently pursue, related to accurate approximation of option prices. Next to the numerical solution of the Black-Scholes equation by means of accurate finite differences and an analytic coordinate transformation, we present results for options under the Variance Gamma Process with a grid transformation. The techniques are evaluated for European and American options.
  • Mathematical Finance Seminar
28 January 2005
14:15
Christian Ewald
Abstract
We discuss the application of gradient methods to calibrate mean reverting stochastic volatility models. For this we use formulas based on Girsanov transformations as well as a modification of the Bismut-Elworthy formula to compute the derivatives of certain option prices with respect to the parameters of the model by applying Monte Carlo methods. The article presents an extension of the ideas to apply Malliavin calculus methods in the computation of Greek's.
  • Mathematical Finance Seminar

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