Efficient Numerical Pricing of American Call Options Using Symmetry Arguments

66 Pages Posted: 30 Apr 2019

See all articles by Lars Stentoft

Lars Stentoft

Department of Economics, University of Western Ontario; Center for Interuniversity Research and Analysis on Organization (CIRANO); Aarhus University - CREATES

Date Written: March 29, 2019

Abstract

This paper demonstrates that it is possible to improve significantly on the estimated call prices obtained with the regression and simulation based Least-Squares Monte-Carlo method of Longstaff & Schwartz (2001) by using put-call symmetry. Results show that the symmetric method performs much better on average than the regular pricing method for a large sample of options with characteristics of relevance in real life applications, is the best method for most of the options, never performs poorly and, as a result, is extremely efficient compared to the optimal but unfeasible method that picks the method with the smallest Root Mean Squared Error (RMSE). A simple classification method is proposed that, by optimally selecting among estimates from the symmetric method with a reasonably small order used in the polynomial approximation, achieves a relative efficiency of more than 98%. The relative importance of using the symmetric method increases with option maturity and with asset volatility. Using the symmetric method to price, for example, real options, many of which are call options with long maturities on volatile assets, for example energy, could therefore improve the estimates significantly by decreasing their Bias and RMSE by orders of magnitude.

Keywords: American Options, Least-Squares Monte Carlo, Put-Call Symmetry, Regression, Simulation

JEL Classification: C15, G12, G13

Suggested Citation

Stentoft, Lars, Efficient Numerical Pricing of American Call Options Using Symmetry Arguments (March 29, 2019). Available at SSRN: https://ssrn.com/abstract=3362426 or http://dx.doi.org/10.2139/ssrn.3362426

Lars Stentoft (Contact Author)

Department of Economics, University of Western Ontario ( email )

London, Ontario N6A 5B8
Canada

Center for Interuniversity Research and Analysis on Organization (CIRANO)

2020 rue University, 25th floor
Montreal H3C 3J7, Quebec
Canada

Aarhus University - CREATES

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

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