Study On European Option Pricing With Regime Switching

Under the background of economic change multiterminal at home and abroad,the macroeconomic analysis system remains the same in the implicit assumption has been more and more cannot satisfy the needs of the reality,so to be able to describe the characteristics of the economy periodic variation,the state transition model arises at the historic moment.Generally speaking,we will set to the state transition process conforms to continuous-time Markov process,will describe the importance of economic dynamic parameter conforms to the continuous time Markov chain.So,obviously,based on the economic background in financial instruments of the option pricing problem,the classic Black-Scholes model,described the move of economic,assumpting the important parameters of the state are constant cannot fully reflect the actual situation.Therefore,the research on introducing institutional transformation into the option pricing model is more and more extensive.Considering the volatility is an important measure of financial market risk,this paper studies the stochastic volatility model with Markov regime switching,namely MS-Heston model.At the same time,in order to take into account the accidental events in the financial market,this article second part studied the jump diffusion model with Markov regime switching,namely MS-SVCJ model.In this paper,on the basis of other scholars research,described the risk-free interest rate and volatility change variable is assumed to be in line with the economic cycle variation characteristics,and number of economic conditions can be divided into two kinds of circumstances and a variety of situations are discussed respectively.In this paper,the alias sampling method was firstly adopted to determine the economic status of each section,then the conditional Monte Carlo(CMC)algorithm was established based on the MS-Heston model and the MS-SVJ model,respectively.On the basis of these,in order to further reduce the variance,the control variates method was included in the CMC algorithm,forming the CMCC algorithm.In addition,two simulation approaches for the MS-SVJ model were discussed,i.e.,the adaptive Monte Carlo(ACMCC)method and the average allocation strategy(AVG).Through analysis it was found that compared to the original Monte Carlo algorithm,the CMCC method and the ACMCC method achieved better error reduction effects.