Perpetual American options in a diffusion model with stochastic interest rates

We present solutions to the perpetual American standard put and call option pricing problems in an extension of the Black-Merton-Scholes model in which the dynamics of the interest rate are described by a mean-reverting... [ view full abstract ]

We present solutions to the perpetual American standard put and call option pricing problems in an extension of the Black-Merton-Scholes model in which the dynamics of the interest rate are described by a mean-reverting Ornstein-Uhlenbeck process. The method of proof consists of reducing the original optimal stopping problems to the equivalent elliptic-type free-boundary problems and applying the smooth-fit principle for the value functions at the optimal exercise boundaries for the underlying assets. We derive closed-form expressions and some explicit estimates for the value functions and prove that the optimal exercise boundaries provide unique solutions of the appropriate nonlinear integral equations.