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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.
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