High-Performance American Option Pricing

50 Pages Posted: 2 Aug 2016

See all articles by Leif B. G. Andersen

Leif B. G. Andersen

Bank of America Merrill Lynch

Mark Lake

Bank of America Merrill Lynch

Dimitri Offengenden

Strategist

Multiple version iconThere are 2 versions of this paper

Date Written: August 1, 2016

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.

Keywords: american options, integral, computational finance

Suggested Citation

Andersen, Leif B.G. and Lake, Mark and Offengenden, Dimitri, High-Performance American Option Pricing (August 1, 2016). Journal of Computational Finance, 20(1), 39-87, DOI:10.21314/JCF.2016.312 . Available at SSRN: https://ssrn.com/abstract=2816818

Leif B.G. Andersen (Contact Author)

Bank of America Merrill Lynch ( email )

One Bryant Park
New York, NY 10036
United States
646-855-1835 (Phone)

Mark Lake

Bank of America Merrill Lynch ( email )

One Bryant Park
New York, NY 10036
United States

Dimitri Offengenden

Strategist ( email )

United States

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