Reset Option Pricing With Power Payoff Under Stochastic Interest Rate

As the development of financial markets, a number of path-dependent options come out. As a classical path-dependent options, reset option becomes more and more popular since1990s. In reset options, the strike shall be reset to the smaller value between the previous strike and the price of underlying assets on the prespecified reset dates. On the one hand, the structure of interest rates plays crucial role in financial asset pricing; on the other hand, power payoff helps to improve the payoff structure and offer option holders the opportunity to get more profits. Therefore, the paper assumes interest rate follows extended Vasicek model and provides closed-form pricing formulas of reset options. In the paper, using Girsanov Theorem and martingale method, two new measures are constructed and the pricing formulas was derived for reset options with single reset date: Furthermore, the method is adopted to the pricing of reset options with multiple reset dates and closed-form pricing formulas in different intervals are derived through a series of transformations of multidimensional normal variables.