The Free Boundary for the American Put Option

Abstract

The free boundary of the American put option is analytically characterized via new and exact formulae. New, accurate short-time asymptotics are an immediate corollary of these analytical results. The free boundary is also represented formulaically throughout all tenors by a simple two-parameter generalized Gaussian functional form.

TOPICS: Options, fundamental equity analysis, statistical methods

Key Findings

• • First exact formula for the free boundary (early exercise boundary) of the American put option in terms of the exogenous inputs: risk-free rate, volatility, and a boundary dependent integral.

• • A simple and accurate asymptotics formula for the free boundary of the American put option near expiration.

• • An empirical solution (possibly exact) of the free boundary as a two-parameter generalized Gaussian functional form.