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

Abstract

In <b><i>Testing and Mapping an Empirical Exercise Boundary for the American Put Option</i></b>, from the Fall 2021 issue of <b><i>The Journal of Derivatives</i>, Joe Pimbley</b> of <b>Maxwell Consulting</b> tests a new streamlined method for calculating the early expiry boundary of American put options. The new method is an analytic solution recently developed by Thomas Little (2020), which appeared in the Winter 2020 issue of <i>The Journal of Derivatives</i>. The problem relates to determining the optimal time at which to exercise an American put option. This was viewed as one of the seemingly unsolvable problems of modern finance. Until now, market participants have used a variety of cumbersome numerical approximations to address the issue. Pimbley found that Little’s method would enable a dealer to make better trading decisions and avoid arbitrage by quickly revaluing and determining the risk sensitivity of a large book of options. However, because Little’s method relies on an initial educated guess (an <i>ansatz</i>), which Pimbley could not independently replicate, it is not possible to fully explain why Little’s methodology is effective.