The Arbitrage Free Pricing Of Two Types Of Random Claims

This thesis mainly studies the pricing and hedging problems of variable annuities with guaranteed benefits and non-guaranteed corporate bonds(i.e.,Unsecured Cor-porate Bond).Actually,based on arbitrage free framework,by analysing influencing factors and cash flows of the products,we discuss the pricing of guaranteed mini-mum death benefits(GMDB),the hedging of guaranteed minimum withdrawal benefits(GMWB)and the pricing of corporate bonds,and then give closed-form solutions of their values.indicatesFor the GMDB,assuming that there are stochastic interest rate and the risky asset with stochastic volatility in the financial insurance market,we first set up a framework for pricing inflation-linked derivatives.Under this framework,we study the fair values of two typical inflation-linked GMDBs by analysing cash flows.Then,by splitting the annuity contract into a portfolio of Arrow-Debreu securities and using measure transformations,we derive closed-form solutions of the values of GMDBs with the inflation guarantee and compound guarantee.Furthermore,we also give an elaborate numerical analysis which contains the parameters’ impacts on the values of GMDB contracts.The numerical results show that the death benefit of inflation guarantee is slightly overpriced in constant volatility of stock situationFor the GMWB,we establish a risk management mechanism for insurance com-panies in the complete financial market that includes bonds and risky assets,and the mechanism is conducive to better management of risks by insurance companies.As-suming that insurance companies adopt the quadratic objective function and establish three accounts for a GMWB contract:the policy holder’s asset account,liability ac-count,hedging account,the problem of hedging risks in GMWBs can be transformed into asset liability management problem.Then,we not only can easily obtain the fair rate,but also can derive the closed-form solution of optimal strategy by solving 3N backward stochastic differential equations(BSDEs).In addition,we perform detailed sensitivity analysis on the new model,such as the effects of parameters on the optimal strategy,etc.For the non-guaranteed corporate bond,assuming that default will occur when equity is insufficient to make up for the instantaneous loss,by combining with the arbitrage free Nelson-Siegel model,we propose a four-factor model for bankruptcy intensity.Afterwards,by introducing fewer parameters,we can establish a flexible,arbitrage free yield curve model which indicates that the yield curve can have multiple shapes.Finally,based on the idea of Kalman Filter method,we construct a stable method for estimating parameters in our model,and study the model s performance in China market,i.e.,we use market data to take the out-of-sample forecast on yields and credit spreads.The results show that the mean regression characteristic in credit spread model is reasonable,and the arbitrage free credit spread model we proposed is superior to the random walk model in forecasting corporate bond yields and credit spreads.