Closed Form Optimal Exercise Boundary of the American Put Option

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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.

Original languageBritish English
Article number2150004
JournalInternational Journal of Theoretical and Applied Finance
Issue number1
StatePublished - Feb 2021


  • American put option
  • free-boundary problem
  • geometric Brownian motion
  • integral equation
  • optimal stopping


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