PT  - JOURNAL ARTICLE
AU  - Thomas Little
TI  - The Free Boundary for the American Put Option
AID  - 10.3905/jod.2020.1.114
DP  - 2020 Nov 30
TA  - The Journal of Derivatives
PG  - 9--21
VI  - 28
IP  - 2
4099  - https://pm-research.com/content/28/2/9.short
4100  - https://pm-research.com/content/28/2/9.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.