Contingent Option Pricing In A Non-markovian Regime-switching Jump-diffusion Model

The pricing problem of guaranteed minimum death benefit(GMDB)is a hot topic in insur-ance and finance.Consider the guaranteed minimum death benefit of a GMDB rider,through taking conditional mathematical expectation,this problem can be transformed into solving the pricing problem of a contingent option.Since the above question is of practical significance,the main purpose of our thesis is to select an appropriate asset price model,and then calcu-late the fair pricing of contingent options with settlement date T_xand settlement price K in a Non-markovian Regime-switching Jump-diffusion Model.We assume that the underlying asset price follows a Non-markovian Regime-switching Jump-diffusion Model,which is driven by a Markov chain.The model coefficients are mea-surable and adaptive to the filtration generated by the Markov chain.These coefficients may depend on the historical path of the Markov chain.This differentiates our model from the com-mon Markovian Regime-switching model,whose model coefficients only relate to the current state of the Markov chain.Non-markovian Regime-switching Jump-diffusion Model combines the advantages of Markovian Regime-switching model and Jump-diffusion model,and possess the feature of path dependence at the same time,which can better fit the real market.To get the fair value of contingent options,the difficulty lies in calculating the density func-tion of underlying asset prices,so we try to get its moment generating function.By using BSDE and Ito's formula,we obtain the semi-analytical expression of moment generating function in the Non-markovian Regime-switching Jump-diffusion model.By strengthening the assump-tions,we consider three special cases of the model:Markovian case,continuously-monitored averaging case and delay case.For these three special cases,the analytical expressions of mo-ment generating function are derived,and then the pricing theorems are given by using moment generating function and Laplace transform.The part of numerical simulations is finished in matlab.First,we regulate the distribution parameters of variable T_xaccording to the experi-ence life table.And then,under different cases,we use Gaver-Stehfest algorithm to do the inverse Laplace transform on the pricing formulas to obtain the numerical results of the fair value of contingent options.We mainly compare and analyze the results of Markovian case and delay case.