High Performance American Option Pricing
43 Pages Posted: 11 Jan 2015 Last revised: 12 Aug 2015
Date Written: July 1, 2015
We develop a new high-performance spectral collocation method for the computation of American put and call option prices. The proposed algorithm involves a carefully posed Jacobi-Newton iteration for the optimal exercise boundary, aided by Gauss-Legendre quadrature and Chebyshev polynomial interpolation on a certain transformation of the boundary. The resulting scheme is straightforward to implement and converges at a speed several orders of magnitude faster than existing approaches. Computational effort depends on required accuracy; at precision levels similar to, say, those computed by finite difference grids with several hundred steps, the computational throughput of the algorithm in the Black-Scholes model is typically close to 100,000 option prices per second per CPU. For benchmarking purposes, Black-Scholes American option prices can generally be computed to at 10 or 11 significant digits in less than one-tenth of a second.
Keywords: American option pricing, integral equations, fixed point algorithm, Chebyshev interpolation, collocation methods
JEL Classification: C60, C63, G12, G13
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