The American put with finite‐time maturity and stochastic interest rate
研究了Black-Scholes市场中随机利率下有限期限美式看跌期权的定价，证明了期权价值的光滑性、提前行权溢价公式及最优行权边界的存在性，并给出了数值解。
Abstract In this paper, we study pricing of American put options on a nondividend‐paying stock in the Black and Scholes market with a stochastic interest rate and finite‐time maturity. We prove that the option value is a C 1 function of the initial time, interest rate, and stock price. By means of Itô calculus, we rigorously derive the option value's early exercise premium formula and the associated hedging portfolio. We prove the existence of an optimal exercise boundary splitting the state space into continuation and stopping region. The boundary has a parametrization as a jointly continuous function of time and stock price, and it is the unique solution to an integral equation, which we compute numerically. Our results hold for a large class of interest rate models including CIR and Vasicek models. We show a numerical study of the option price and the optimal exercise boundary for Vasicek model.