Title: Barrier options in three dimensions

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.

DOI: 10.1504/IJFMD.2014.059642

International Journal of Financial Markets and Derivatives, 2014 Vol.3 No.3, pp.260 - 292

Received: 15 Feb 2013
Accepted: 08 Nov 2013
Published online: 30 Jun 2014 *

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