Pricing Of Exchange On Power-Option With Interest Payment Based On ARIMA-GARCH Model

In 1973, Black and Scholes proposed the option pricing model of the stock that follows geometric Brown motion. The model has advantage and disadvantage:the advantage is good at calculating, the disadvantage is assumed that the drift and volatility of stocks is constant. From then on, many scholars are committed to search how to use drift and volalitity of stock to pricing contingent claim. Which have been approved is the major in this paper-ARIMA-GARCH model. ARIMA-GARCH model is an effective method in predicting volatility of Black-Scholes option pricing model. The option showed its unique charm and became the most dynamic derivative financial products, has been rapid development and wide application. In order to competition and attract investors, financial institutions have launched some new options, and the most popular can reduce the rights of payment options. Exponential is one of the innovative options, which can change the income structure of the innovative options, and more flexible than the standard options, enough to adapt to different risk preferences of investors requirements.This paper mainly focus on the pricing of interest rate derivative securities in the financial mathematics, Consider the rate of assets return, when the drift and volatility are constant or time variable parameters, refers to the ARIMA-GARCH time series model and the random function Vasicek stochastic interest interest rate model pricing of contingent claims. The following are this paper's main results and innovations:(1) Establishment drift rate and volatility ARIMA-GARCH martingale process, through the time set of the financial information, modified parameters of stochastic differential equations with bonus.(2) Improve the accuracy of pricing diffusion equation under the random imcome of ARIMA-GARCH martingale process, pricing Exchange Options with power payoffs.(3) Given the method and proof of the multidimensional joint Brownian motion into one-dimensional Weiner process; and then, through the above method deal the relevance Vasicek stochastic interest rate and a joint diffusion process of stock; lastly, getting the pricing model with exchange power option payoffs under Vasicek stochastic interest.