Optimal Stopping And American Option Pricing

Options are a kind of financial innovative instrument which came into being in the mid-1970s in America. As a better means for prevent financial risks, they have developed quickly in the past two decades and more. According to transaction time, options can be divided into two sections; American options and European options. American options give the holder the right to exercise the option at or before the expiry date, so American options are commonly used. In the international financial market, American options transactions are more dynamic, especially in the market of stock options. The holder can exercise the option prior to expiry, so the payoff of American options is governed not only the price of underlying assets at maturity but the price path. This characteristic of American options renders solutions to value them and determine optimal exercise moment somewhat difficult. What investors are concerned about most are these problems. In this paper, we consider the optimal stopping problem and pricing of American call options. Optimal stopping of standard American options is N in the model of discrete time; optimal stopping of standard American options is maturity in the model of continuous time, and optimal stopping of perpetual American call options doesn't exist. We also discuss the optimal stopping problem of perpetual American call options when stock prices follow a jump-diffusion process, the Optimal stopping is(?)and the initial value isC~*=(?)...