Inversion Algorithm Of Implied Volatility Based On European Option Pricing Model

The assumption that the implied volatility is constant in the classic Black-Scholes option pricing model(B-S model)is not consistent with the financial market.In fact,the implied volatility of an option is a function of the price S and the time t.In this dissertation,the concept of implied volatility base surface and fluctuation volatility is proposed in order to construct the implied volatility function 1/2?2=1/2f02(y,?)+f1(y),where f0(y,?)=?0+?1?+?2y is the volatility base surface and the f1(y)is fluctuation volatility.Taking 50ETF option as a example,its implied volatility is achieved by simultaneous idenfication of both base surface and small fluctuation.And the error of this algorithm is analyzedThis dissertation consists of four chaptersThe first chapter introduces the research background and significance of the implied volatility in the option pricing model.And the research progress for the implied volatility of the options in China and abroad are illustrated.The ana-lytical formula theory and numerical approximation of the implied volatility are summarized.And the analytical formula solution only performs well for at-the-money.The implied volatility linearization model presented by Isakov is of great reference significance,based on which,a base surface-floating volatility inversion strategy is prosposed to reconstruct the implied volatility of optionIn the chapter two,derivations of the classical B-S model are firstly deduced By the Crank-Nicholson difference(C-N difference)scheme,the numerical solu-tion of the option price is obtained with constant volatility.Comparation with analytical solution of the pricing formula is implemented,which validate the con-clusion that C-N difference scheme is stable when ? is a constant.In addition.under the assumption that the implied volatility ? is a function related to the time t and the underlying asset price S,a numerical solution of the option price is achievedIn the chapter three,aiming at inverse problem of reconstructing implied volatility,an inversion strategy of the base surface-fluctuation volatility identifi-cation is proposed.The stepwise regression algorithm is used to reconstruct the implied volatility base surface f0(y,?)=?0+?1?+?2y.Meanwhile the fluctuation volatility f1(y)is reconstructed by the derived integral equation,which are dis-cretized by the complex trapezoidal formula,and stably solved by the Tikhonov regularization algorithm.The simultaneous identification of f0(y,?)and f1(y)may result in the numerical reconstruction of the implied volatility of the option pricing problemIn the chapter four,the financial significance of the base surface-fluctuation volatility inversion strategy is summarized.For the future work with respect to the floating volatility inversion,numerical algorithm can be improved for a better breakthrough.