Barrier options in three dimensions
by Marcos Escobar; Sebastian Ferrando; Xianzhang Wen
International Journal of Financial Markets and Derivatives (IJFMD), Vol. 3, No. 3, 2014

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.

Online publication date: Mon, 30-Jun-2014

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