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A fast algorithm for numerical solutions to Fortet's equation

✍ Scribed by Gorazd Brumen

Book ID
104005701
Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
227 KB
Volume
220
Category
Article
ISSN
0377-0427

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✦ Synopsis

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 M?1 firms and N discretization points in every dimension the algorithm uses O(n log n β€’ M β€’ M! β€’ 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.

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