Applications Of Markov Processes In Pricing Of Life Insurance Products And Credit Derivatives

Markov processes are widely used in the pricing of financial products.Markov chains can be used to represent macroeconomic state variables and describe default indicator processes of companies.In this paper,under the framework of reduced-form models,we use Markov processes to study the pricing of life insurance products and credit derivatives.The main research work is as follows:Firstly,we introduce the shot-noise process with regime-switching into the two-dimensional Markov regime-switching jump-diffusion model to establish a mortality dependent model.The mortality dependence is determined by the economic environment,the dependence of diffusion term and the common jump.The joint Laplace transform of the mortality process is obtained by the martingale method.On this basis,an explicit expression of the price of the life insurance product is derived,which depends on the dependent mortality process of married couples,and a numerical analysis is carried out to illustrate the model.Secondly,we study the change of the total valuation adjustment of credit default swap contracts held by investors when they switch from bilateral credit support annex clearing to central counterparties clearing.First,a general pricing framework for the total valuation adjustment of credit default swap contracts cleared by bilateral credit support annex or central counterparties is established.Then,a four-dimensional Markov copula model with regime-switching is established to describe the default correlation.On this basis,the explicit expression of the total valuation adjustment of credit default swap contracts with bilateral counterparty risk is given,and the theoretical results are illustrated by numerical analysis.