Pricing Of The Lookback Options Under Stochastic Interest

Option because its can and provides a set of time for the investor to guarantee the value function not to lose the profit opportunity but to grow in the tool in the finance to hold the important status. And the option pricing always is a financial mathematics basic question.In order to satisfy the finance market and the more different investors' demand, the scholars utilized options price theory and the analysis method, desighed more different characteristic options.Lookback option is this kind of path-dependent options,makes a final decision the price to rely on certain period of time.At the same time, in the option pricing question, as a result of market instability, even if is the short-term interest rate also is unceasingly changes. Therefore,the hypothesis interest rate is invariable in option term of validity, is insufficient to satisfy the actual background the request, thus must consider the interest rate the determinism to does not grow the property price the influence.This article applies the equivalent martingale measure, the Ito formula, principle of reflection and stochastic differential equation, will discuss pricing options under stochastic interest. Below mainly does the research work: First, used the equivalent martingale measure, transformation and the risk neutral discount method in under the basic B-S option pricing model, obtains the formulas of pricing lookback options under stochastic interest. Second, under interest rate obeys the Vasicek process, we obtains the formulas of lookback options, using the risk neutral discount method .further promotes Goldman's formula of lookback options.