PT - JOURNAL ARTICLE
AU - Little, Thomas
TI - The Free Boundary For The American Put Option
AID - 10.3905/jod.2020.1.114
DP - 2020 Aug 31
TA - The Journal of Derivatives
PG - jod.2020.1.114
4099 - http://jod.pm-research.com/content/early/2020/08/31/jod.2020.1.114.short
4100 - http://jod.pm-research.com/content/early/2020/08/31/jod.2020.1.114.full
AB - 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 methodsKey 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.