Comparative Study Of Credit Spreads Under The Single Factor And Two Factor Stochastic Volatility Models

Recent years,the credit risk of the corporate bond is more and more serious so that the investors are paying more attention to it when they do the investment about the corporate bond.However,the credit risk is a qualitative indicator,which the investors can measure by investigating the asset and liability structure of the corporate,credit rate of the bond or even the moral quality of the issuers to help them decide whether they should do the investment.But it is obviously limited.So more and more scholars are trying to quantify the credit risk to make it become an indicator that can be characterized with objective historical data.The credit spread is undoubtedly a preferred point for credit risk quantification research.What we all know is that the credit spread exists to compensate for the risk of bond default after issuing.It is also the additional benefit that the corporate promises to investors,which is higher than government bonds with the same maturity.Constructing credit spread model provides an effective way to quantify the credit risk of bonds,thus making investors more objective and accurate in judging investment risk of corporate bonds.The Merton model is the most classic model for studying the credit spread.An important idea of the model is to regard the bond as a European put option with the company's assets as the target,and then price the bond through the option pricing method.However,the Merton model assumes that the volatility of the company's assets is constant.Considering the change of the implied volatility over time,many scholars have proposed a volatility model based on the Merton model to describe the changes of the company's assets over time more accurately,so as to find a better credit spread model that can describes the realities of the bond market.In this paper,two models are constructed in terms of bond pricing,which are single factor stochastic volatility model and two-factor stochastic volatility model.In the two-factor stochastic volatility model,each parameter is distinguished between short-term and long-term,so as to study whether the two-factor model can more fully describe the term structure of the credit spread than the single-factor model.This paper hopes to find a way to price bonds more accurately by comparing the two models,so as to get a credit spread model that is closer to the actual market situation.After determining two pricing models,the paper firstly numerically simulate the credit spread curves of the two models by Matlab,finding that the credit spread under the two-factor model is more sensitive to time changes.Then we conduct sensitivity analysis on each parameter of the two-factor model to determine the reason why the two-factor model is more sensitive to the term structure of the credit spread.Finally,this paper uses the actual bond market data to estimate the parameters in the two models and conducts relevant empirical analysis,using the actual data to verify the numerical simulation results.In the China Bond Information Network,we select the market yield of China Bond corporate bonds with AAA,AA and A credit ratings on June 26,2018,and the government bond market yield on June 26,2018.For AAA-level bonds,the debt-to-debt corporate bond is taken at 45% of the debt,for the AA-class bonds,the debt-to-debt corporate debt is 55%,and for the A-grade bonds,the debt-to-debt corporate debt is 70%.In order to make up for the shortage of sample data,this paper uses the interpolation method to obtain the missing rate of return.When calculating,it takes α = 0.5.Using these data,the parameters of the two models are estimated by the calibration method in Matlab,and then the estimated parameter values are brought back to the model,after which,we use Matlab to obtain a comparison chart of the credit spreads of the three credit rating bonds under the two models and the actual market credit spreads.