aIFMF, Department of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenija
Abstract:
A fast algorithm for computation of default times of multiple firms in a structural model is presented. The algorithm uses a multivariate extension of the Fortet's equation and the structure of Toeplitz matrices to significantly improve the computation time. In a financial market consisting of M1 firms and N discretization points in every dimension the algorithm uses O(nlogn·M·M!·NM(M-1)/2) operations, where n is the number of discretization points in the time domain. The algorithm is applied to firm survival probability computation and zero coupon bond pricing.