Authors: Marcos Escobar; Sebastian Ferrando; Xianzhang Wen
Addresses: Department of Mathematics, Ryerson University, Toronto, M5B 2K3, Ontario, Canada ' Department of Mathematics, Ryerson University, Toronto, M5B 2K3, Ontario, Canada ' Toronto Dominion Bank, Toronto, M5K 1A2, Ontario, Canada
Abstract: The paper provides closed-form expressions for the price of several barrier type derivatives with a three-dimensional geometric Wiener process as underlying. These solutions are found for special correlation matrices and are given by linear combinations of three-dimensional Gaussian cumulative distributions. The method of images is used as a key technique to establish the solutions. Two cases are described extending the results to a wider set of correlation matrices, one case deals with random variances and the other case with random correlations.
Keywords: method of images; 3D Wiener process; distribution of minimum; maximum; financial derivatives; barrier options; random variances; random correlation.
International Journal of Financial Markets and Derivatives, 2014 Vol.3 No.3, pp.260 - 292
Available online: 04 Mar 2014Full-text access for editors Access for subscribers Purchase this article Comment on this article