Pricing European Power Exchange Option Under Bidimensional Hawkes Jump Diffusion Process

Exchange options is one of important exotic options that has a wide range of applications such as risk management,portfolio construction,and international trade.In addition,many financial contracts embed exchange options or can be equivalent to exchange options,and economic decision-making is often applied to the concept of exchange options.Since the reasonable pricing of exchange options is an important prerequisite for the correct understanding of it and the effective use of it,it has important theoretical significance and reality value how to rationally model exchange options in the real market environment and then accurately price it.Since the widely adopted Black-Scholes model does not consider asset price jumps,while the Poisson jump diffusion model does not take into account self-stimulation and cross-stimulus effects of the asset prices widely found in recent empirical studies.Unlike the Poisson process,Hawkes process can portray the stimulating effects of asset price jumps.Therefore,this paper will study the European power exchange option pricing problem based on the two-dimensional Hawkes jump diffusion model.First of all,the characteristic function of the Hawkes jump diffusion process is solved under the framework of affine jump diffusion model.Then based on the risk neutral pricing principle,solve the price formula of European power exchange option by transforming the pricing unit and Fourier transform,etc.Since the price process of the underlying assets and the option price formula contain many parameters,then the parameters are classified and estimated with different methods.The POT method and the maximum likelihood estimation method are used to es timate the parameters related to the jump amplitude.Use the Sampling Importance Resampling Particle Filter algorithm estimates parameters related to jump intensity.Finally,based on the pricing formula of European power exchange option,the numerical analysis of option price is carried out by using the analysis method of common Greek letters.First of all,the analytical formula of the price of the European power exchange option is obtained.Secondly,through the numerical analysis,the relationship between the model parameters and the price of the European power exchange option are obtained,the model parameters include ones related to drift diffusion,ones related to the jump intensity and ones related to the jump amplitude.