Pricing Inflation Products With Markov Regime-switching Jump-diffusion Models

The Markov regime-switching model is widely used in the fields of finance and insurance.In this model,the state change of continuous time Markov chains is used to describe the change in the external macroeconomic environment.In order to characterize the phenomenon that interest rates and inflation rates in financial markets are affected by random events,emergen-cies and changes in the macro environment,this article combines the Markov regime-switching model with the jump diffusion model,and considers the the pricing of inflation index swap and swapation under this framework.This article first generalizes the HJM forward interest rate term structure and the CPI in-dex（jump）diffusion model to the Markov regime-switching jump diffusion model,and gives stochastic differential equations of several zero coupon bonds p_r（t,T）,p_n（t,T）and p_IP（t,T）in the inflation market under this framework.Girsanov measure transformation is used to give the martingale condition of the market without arbitrage.First,the method of changing of nu-meraire is used to give the pricing formula of Zero Coupon Inflation Index Swap（ZCIIS）,and the strategy of hedging with nominal bonds p_n（t,T）and inflation-protected bonds p_IP（t,T）is given.With the help of measure transformation,It（?）formula and constructing exponential martingale,we then give the pricing formula of Year-on-Year Inflation Index Swap（YYIIS）.At the same time,the differences in pricing under the filtration F and G are compared.Finally,the pricing formula of Zero Coupon Inflation Index Swaption（ZCIISO）is given using methods such as changing of numeraire and Fourier inverse transformation.