A fast algorithm for numerical solutions to Fortetʹs equation

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 Fortetʹs equation and the structure of Toeplitz matrices to significantly improve the computation time. In a financial market consisting of M ⪢ 1 firms and N discretization points in every dimension the algorithm uses O ( n log n · M · M ! · N M ( 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.