The Application Of Stochastic Differential Equation In Option Pricing

This paper mainly finished the following jobs with the theory of stochastic equation and financial market.(1) Discussed the existing problem of arbitrage about an portfolio in an unequilibria market,on the base of Delbaen and Schachermayer's rearch work (1994,1995,1997),I got some improvements on them.First defined the equivalence martingale measure,then used the character of martingale measure,under the condition of weak market,got a existence and determinable theorem of no arbitrage about an portfolio.(2) On the base of Harrison,Pliska(1983) and Jacod's rearch work(1979)(A market is a compete a market if and only if there exists an equivalence martingale measure in the market),In this paper,I used some knowledge about line space got another further simple determinable theorem about a market's completeness.(3) Discussed the problem of option pricing under the condition of a market's completeness got the option's exact hedging trade formula.(4) With the fixed conditions of the Black-Scholes formula,improved the European price formula and combined the character of America option,concluded that under the same condition,call America option price equals call European option price.(5) Because there is no standard method on computing America put option in the world by now. In order to express all the aspects,I introduced some representative but very useful numeral reckon methods on America put option.(6)Introduced some financial models and functions which is closely related to pricing option.In order to use these functions freely,I gave some procedures about these functions with language of Pascal.