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Special Semester on Stochastics with Emphasis on Finance
Linz, September 2008 - December 2008
Presentation: Numerical solution of an SPDE arising in credit modelling

Workshop: Computational Methods with Applications in Finance, Insurance and the Life Sciences AND Stochastic Methods in Partial Differential Equations and Applications of Deterministic and Stochastic PDEs

Time: Wed, November 19, 2008, 16:20-17:10

Speaker: Christoph Reisinger

Abstract

The firm value distribution in a large (credit) portfolio can be approximated by the solution to a stochastic partial differential equation (SPDE). We motivate this limit and use it to compute tranche spreads for basket credit derivatives. A naive Monte Carlo solver on top of a PDE solver is computationally costly, and therefore attention has to be paid to the implementation of default events, boundary conditions, and data smoothing, to ensure fast convergence. The reduced set of effective parameters can be calibrated to the firms' individual credit default swaps and to observed tranche prices for basket products.

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