Pricing Of The Maximum Or Minmum Option In Jump Diffusion Model With Stochastic Interest Rate

With the continuous development of economy,forward contracts,futures,options and other financial derivatives have been favored by many derivative traders.As one of the most important financial derivatives,option has attracted more and more attention,so its pricing has become one of the core problems in financial mathematics.The standard B-S option pricing model assumes that the trading market is a nonarbitrage,balanced,and complete market,but the actual trading market is arbitrage,uneven,and incomplete.Therefore,many scholars have extended the B-S model.For example,the interest rate?the drift rate and the volatility rate are extended to deterministic functions of time;the interest rate is assumed to obey the Vasicek interest rate model;the compound Poisson process describing the change of asset price is added to the asset price process and etc.These assumptions make the option pricing model more in line with the actual trading market and have stronger applicability.The maximum or minmum option is a new type of option,discussing the maximum or minimum option of two or more underlying assets.In this paper,we study the pricing of the maximum or minimum option under different models by Girsanov theorem and measure transformation.The main contents are as follows:Firstly,assuming that the underlying asset price follows the geometric Brownian motion under the jump diffusion model and the interest rate r(t)follows the extended Vasicek model,we get the pricing formula of the maximum or minimum option by actuarial approach,and give the influence of related variable on option by Matlab.Secondly,assuming that the underlying asset follows the multidimensional geometric Brownian motion under the jump diffusion model,the fixed price follows the multidimensional geometric Brownian motion,and the interest rate r(t)follows the extended Vasicek model,we get the pricing formula of the maximum or minimum option with uncertain price by Girsanov theorem under the jump diffusion model and measure transform,and give the influence of related variable on option by Matlab.Moreover,assuming that the underlying asset price follows the geometric fractional Brownian motion under the jump diffusion model and the interest rate r(t)follows the extended Vasicek mode,we get the pricing formula of the maximum or minimum option by fractional Girsanov theorem under the jump diffusion model and measure transformation,and give the influence of related variable on option by Matlab.