Valuation of foreign currency options under stochastic interest rates and systematic jumps using the Martingale approach
Abstract
This research studies the valuation of spot, forward, and futures options on foreign exchange when the underlying variables follow jump-diffusion processes. The domestic and foreign term structures of interest rates are used to hedge the systematic jumps in the spot exchange rate as described by Jarrow and Madan (1992). The methodology is based on the equivalent martingale measure technique of Heath, Jarrow, and Morton (1992). The analysis generalizes Amin and Jarrow's (1991) model for currency options to include systematic discontinuities. A closed-form solution for European options is derived under the assumption of constant volatilities and binomial Poisson risk. The implementation of this formula is complex but reasonably fast. Numerical results show that the jump component can significantly affect option prices. An extensive comparison with extant models show that our model can potentially explain empirical biases on the pricing of currency options.
Degree
Ph.D.
Advisors
McConnell, Purdue University.
Subject Area
Finance|Mathematics
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