The Study Of European Option Pricing With Residual Risk

With the development of economy, Classical Black-Scholes option pricing formula isdifficult to meet the needs of the reality, For it is obtained under a series of strict assumptions,did not consider the effect of residual risk for option pricing. When considering residual risks,it can be better close to the actual, making pricing formula more flexible. There haveimportant theoretical and practical significances to evade, manage financial risk and correctprice the options.Higher-order moments are important consideration in option pricing and in valuingportfolios under the assumption of a discrete-time trade case and absence of transaction costs.In this paper we study the impact of the stock return third-moment residual risk on Europeanoption pricing. Through mean self-financing and variance-minimizing hedging criteria wederive that the valuation of a European option satisfies a third order partial differentialequation with respect to the stock price; The closed-form solution for this partial differentialequation has been obtained by means of the Fourier transform, which will collapse to theBlock-Scholes formula as the time scaling converges to zero. In particular, we get thegeneralization of the Delta hedge strategy; we also find that the third-moment residual riskand the risk, preferences of the traders play an important role in option pricing and in portfoliohedging.