Numerical Methods for American Spread Options under Jump Diffusion Processes
This paper examines two numerical methods for pricing of American spread options in the case where both underlying assets follow the jump-diffusion process of Merton (1976). We extend the integral equation representation for the American spread option presented by Broadie and Detemple (1997) to the case where the return dynamics for both underlying assets involve jump terms. By use of the Fourier transform method, we derive a linked system of integral equations for the price and early exercise boundary of the American spread option. We also provide an integral equation for the delta of the American spread option, and determine the limit of the early exercise surface as time to expiry tends to zero. We consider two numerical methods for computing the price, delta and early exercise boundary of the American spread option. The first method is a two-dimensional generalisation of the method of lines for jump-diffusion, extending on the algorithm of Meyer (1998). The second method involves a numerical integration scheme for Volterra integral equations. This algorithm extends the methods of Kallast and Kivinukk (2003) and Chiarella and Ziogas (2004) to the two-dimensional jump-diffusion setting. The methods are benchmarked against a suitable Crank-Nicolson finite difference scheme, and their efficiency is explored.
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