Journal of Computational Finance

Risk.net

High-performance American option pricing

Leif Andersen, Mark Lake and Dimitri Offengenden

  • Pricing American options via integral equations can be fast and accurate.
  • When properly formulated as a fixed-point collocation problem, the method can beat other numerical methods by many orders of magnitude.
  • Achieving such performance is dependent on a proper representation of the boundary.
  • The method can be used to obtain high pricing throughput or for establishing high-precision benchmark values.

ABSTRACT

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 a finite-difference grid 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 ten or eleven significant digits in less than one-tenth of a second.

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