Pricing Permanent American Options Under Stochastic Interest Rate

Due to the further increase of economic globalization and diversification,there are more and more unstable factors and investors’ demands in the market.In order to meet the changes of the market and the needs of investors,a large number of new options have been designed and put into the market,so it is more urgent to study the pricing of options.Among these new types of options,most of them are American options that can be exercised at any time and barrier options that depend on price path.Therefore,the pricing of these two kinds of options is an important aspect of financial mathematics and financial derivatives research.Compared with the option pricing with constant interest rate,the option pricing with stochastic interest rate has higher reference value because it can better simulate and correspond to the interest rate changes in the real market.At the same time,it plays an important role in the practical application of option products to play the best effect and improve the design level of option products.This paper mainly studies the permanent American option and the European put barrier option under the stochastic interest rate model and special price model.In this paper,martingale method of option pricing is used to study the pricing of permanent American option under a special stochastic interest rate model,and get the option price formula under ideal conditions.For the research of European barrier option under stochastic interest rate model,the martingale approach of option pricing is combined with the change of numeraire to form a comprehensive method.Under a special stochastic interest rate model,by using the constructed equivalent martingale measure and equivalent conversion of corresponding conditions,the pricing formulas of two kinds of European barrier options with some conditions are finally obtained,which makes preparation for the pricing research of permanent American barrier options.In this way,it is more convenient to manage financial risks in practical application.