Closed form optimal exercise boundary of the American put option

TL;DR

This paper derives explicit closed-form solutions for the optimal exercise boundary of finite maturity American put options under models with time-dependent parameters, enhancing analytical tractability.

Contribution

It introduces models with time-dependent interest rate, dividend yield, and volatility that allow explicit solutions for the American put option's exercise boundary.

Findings

Explicit closed-form solutions for exercise boundary obtained.

Integral equation for boundary solved analytically.

Models accommodate time-dependent parameters for practical relevance.

Abstract

We present three models of stock price with time-dependent interest rate, dividend yield, and volatility, respectively, that allow for explicit forms of the optimal exercise boundary of the finite maturity American put option. The optimal exercise boundary satisfies the nonlinear integral equation of Volterra type. We choose time-dependent parameters of the model so that the integral equation for the exercise boundary can be solved in the closed form. We also define the contracts of put type with time-dependent strike price that support the explicit optimal exercise boundary.