Testing and Mapping an Empirical Exercise Boundary for the American Put Option

Abstract

Recently published research has identified an empirical approximation to the free exercise boundary of an American equity put option. This article examines the accuracy of this simple, readily calculated approximation through linear regression analyses of hundreds of numerically generated free boundaries. The author finds that this Little Ansatz provides an excellent estimate of the optimal boundary for all meaningful parameter values and times to expiration. A second result of this article is the mapping of the two empirical parameters as functions of risk-free rate and volatility. This mapping is necessary to enable fast option pricing and sensitivity calculations for large books of these derivative transactions. Proper calculation of the American put option is a long-standing challenge that has spawned immensely creative and admirable research. The discovery of this empirical approximation has great practical importance.

TOPICS: Derivatives, options, security analysis and valuation, quantitative methods, statistical methods

Key Findings

• ▪ The author finds that a recently published empirical expression provides an excellent estimate of the American free exercise boundary for all meaningful parameter values and times to expiration.

• ▪ The author determines efficient and accurate mapping of the two necessary adjustable parameters of the approximation as functions of risk-free rate and volatility.

• ▪ The author suggests future research and improvements for this fast, empirical solution to the American free exercise boundary.