The American put with finite‐time maturity and stochastic interest rate

In this paper, we study pricing of American put options on a nondividend-paying stock in the Black and Scholes market with stochastic interest rate finite-time maturity. We prove that option value is C1 function initial time, rate, price. By means Itô calculus, rigorously derive value's early exercise premium formula associated hedging portfolio. existence an optimal boundary splitting state space into continuation stopping region. The has parametrization as jointly continuous time price, it unique solution to integral equation, which compute numerically. Our results hold for large class models including CIR Vasicek models. show numerical price model.