| In financial market,the interest rate is the benchmark for many business,such as asset pricing,product design,risk management and speculation.As an important tool for the central bank to achieve monetary policy,interest rate can adjust social aggregate demand and inflation.At the same time,it can influence the change of bond pricing in financial market.Therefore,it is generally believed that the pricing problem of derivatives is determined by interest rate.With the development of economy,the issue of defaulted bond pricing is widely concerned by scholars from various countries.As the core of derivatives pricing,interest rate is of great significance to the study of defaulted bond pricing.However,when pricing bonds with interest rate,it is possible that interest rate may be negative rate,and the continuity of bond price tends to be destroyed by unexpected events in real financial market.These problems have caused serious problem to the study of bond pricing with default risk.This paper discusses the general equilibrium model which can be used in bond pricing,including the Vasicek stochastic interest rate model and the CIR stochastic interest rate model.Given that the Vasicek interest rate model may present a negative interest rate,this paper studies the CIR stochastic interest rate model,in order to ensure that the interest rate is positive.By using equivalent martingale measure and the Girsanov theorem,the CIR interest rate model with stochastic jump items is established under the risk-neutral measure,which solves the problem of discontinuous change of bond price in financial market.At the same time,the rationality of the model is analyzed.Then,by utilizing the CIR interest rate model with random jump items under the risk-neutral measure,the partial differential equation satisfying the bond price without default risk is studied.Based on the default event and the risk process of martingale,the formula of bond pricing with default risk is given. |
PDF Full Text Request