Pricing foreign equity options under Lévy processes

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Abstract

This article investigates the valuation of a foreign equity option whose value depends on the exchange rate and foreign equity prices. Assuming that these underlying price processes are correlated and driven by a multidimensional Lèvy process, a method suitable for solving the complex valuation problem is developed. First, to reduce the number of dimensions of the problem, the probability measure is changed to embed some dimensions of the Lèvy process into the pricing measure. Second, to simplify the integral complexity of the discounted terminal payoff, the valuation problem is transformed to Fourier space. The main contribution of this study is that by combining these two methods, the multivariate valuation problem is significantly simplified, and very accurate results are obtained relatively quickly. This powerful method can also be applied to other multivariate pricing problems involving Lèvy processes. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:917–944, 2005

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