High Performance American Option Pricing

43 Pages Posted: 11 Jan 2015 Last revised: 12 Aug 2015

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: July 1, 2015

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 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

Suggested Citation

Andersen, Leif B.G. and Lake, Mark and Offengenden, Dimitri, High Performance American Option Pricing (July 1, 2015). Available at SSRN: https://ssrn.com/abstract=2547027 or http://dx.doi.org/10.2139/ssrn.2547027

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

Register to save articles to
your library

Register

Paper statistics

Downloads
1,308
Abstract Views
4,391
rank
14,182
PlumX Metrics