Two-Asset Option Pricing Under A Log Student’s T-Distribution

Classic Black-Scholes option pricing formula is built on a series of strict assumptions.These assumptions are not consistent with the actual operation law in the real financial market,so the pricing results were not ideal when using Black-Scholes option pricing formula inpractice. Therefore, we have to look for other method. This research is the hotpot anddifficulty in mathematical financial, and is also the starting point of this paper.This paper first reviews systematically the research on option pricing. Then brieflyintroduced the useful knowledge of Random process and Behavioral finance, and the historyof the development of the option pricing formula. At last, we introduced the main two-assteoptions and their pricing formulas in the classic Black-Scholes model.The main results are in the following: according to the points of Behavioral finance, underthe hypothesis of bounded rational investors we replaced the normal distribution by Studentt distribution in the classic Black-Scholes model. Through the conditional delta hedgingstrategy and the minimal mean-square-error hedging, a closed-form solution the two-assetoption value is obtained. In particular, we propose a procedure to estimate the volatilityparameter such that the pricing error is in accord with the risk preferences of investors. Inaddition, we discover that scaling laws play an important role in option prizing in this case.About this problem, we has not yet seen the similar paper at present. By a mean-self financingdelta-hedging argument, a two-asset option pricing differential equation is obtained. Then weget the formulas of Better-of options and Out performance options.