Pricing Of Volatility Derivatives Under Heston Model And Its Generalized Model

Recent years,more and more attention has been paid to the management of the volatility risk with the influence of financial crisis.In order to deal with the investors and risk managers' needs of diversified volatility risk management,the volatility derivatives market has expanded rapidly.To effectively provide volatility exposure,volatility and variance swaps are among the most popular trading products.Therefore,this paper mainly discusses the pricing of variance swap and volatility swap under the different models from the following five parts.The first chapter illustrate the significance and purpose of pricing of volatility derivatives in the existing financial markets,and then focuses on the research development of variance swaps and volatility swaps in academic research,finally introduces the main work content and arrangement of this article.In the second chapter,we first recall some basic definitions and important theorems of stochastic analysis,illustrates the concept of Ito integral and Ito's formula,as well as gives the Girsanov theorem,which explains the principle of measure transformation from the theoretical point of view.Secondly,we introduces the risk-neutral pricing method.Finally,the definition of Fourier transformation for pricing problem is given.The third chapter gives brief introduction to the forward contract of the variance swap.Under the two models of Heston stochastic volatility model and the stochastic volatility model with stochastic interest rate,the closed-form of the solution of variance swap pricing formula under discrete sampling is given by using the method of Fourier transformation and the idea of dimension reduction.In the fourth chapter,for giving the pricing formula of volatility swap under the Heston model and the general model with the elastic parameters,we firstly introduce the volatility derivatives such as volatility swap,and then discuss the pricing of volatility swap under the Heston model by using the forward characteristic function approach.This method does not require the specific distribution of volatility process,so it is applicable to the general model.Finally we demonstrate an approximate solution to the pricing formula of volatility swap under the general model.The fifth chapter provide with the numerical solution process by using Euler-Maruyama algorithm.A Monte Carlo simulation method is used to verify the pricing formula obtained from the third and fourth chapters from the angle of numerical simulation,which proves the effectiveness of the pricing formula.