Research On Pricing Of Power European Options By Lévy Process

Option pricing has always been a hot topic in the field of financial research.As a new option,the power option is different from the traditional option.Compared with the traditional option,the value of the power option is more sensitive to the change of the underlying asset price,which amplifies the option risk and is suitable for investors with different risk preferences.Therefore,the study of power options is of great practical significance.At the same time,relative to Brown movement,the Lévy process is the more general movement,which is a stochastic process with stationary increments independent generalized and infinite divisibility,can include continuous diffusion and infinite small jump.It can describe greatly the fat tail and peak characteristics of random distribution.It is more practical to use the Lévy process to model the asset pricing model.Based on the option pricing and Lévy process theory,this paper mainly solves two problems on power European option pricing:First,consindering the randomness and mean-reversion of interest rate and underlying asset,the changing rules of interest rate and stock price with continuous dividend are discribed by Hull-White interest model and exponential Omstein-Uhlenbeck(O-U)process respectively.The pricing problem of a class of power European option is studied by using the changes of numeraire method based on the above models and the continuous dividend.Finally,the pricing formulas of power European options are obtained.It extends the conclusions of the existing literature.Second,The asset price model driven by Lévy processes makes it more general to depict the price of the assets.Relative to Girsanov transform,it is more convenient to find a risk neutral measure P*by Esscher transform.Under P*,finding Fourier transform of the power option with payment function max{ST?-K?,0}.then,the final option price is abtained by inverse transformation of Fourier.Finally,we get the pricing formula of power option driven by a simple Lévy processes.