Research On Integrated Risk Measurement Model For Defaultable Zero-coupon Bonds

Risky positions in trading and banking books of commercial banks, defaultable bonds, over-the-counter portfolios, credit derivatives and so on can be treated as default risk related financial instruments or defaultable assets, and defaultable asset or portfolios face market risk and credit risk simultaneously. Under the ERM framework, we should manage overall or comprehensive risk. If we consider only one type of risk and ignore the other, obviously, the risk management can not be complete and good, especially when the two types of risk are both playing important roles. However, the traditional Enterprise-wide Risk Management treats types of risk separately and the necessary amount of economic capital is determined for each risk type, neglecting the relation of the two types of risk. Recently, however,a large number of studies have indicated that the credit risk and the market risk are related with each other, so we discuss the method of integrated-risk measurement in order to manage the risk more precisely and in detail.This paper takes defaultable zero-coupon bonds as the research target, which simultaneously faces two main types of risk, namely, credit risk and market risk (interest risk). Contrary to the traditional approach of measuring different risk separately, we study the integrated-risk and build an integrated risk measurement model for the defaultable zero-coupon bond. Also, the empirical analysis is presented.Firstly, we recognize the two main types of risk, that is credit risk and interest risk, discuss the interaction among the factors of interest risk and credit risk, including default, rate of loss given default and exposure at default. Unlike considering only one type of risk or simply adding after measuring different risks separately or the way to connect the two risk types by Copula functions, we propose a general framework of integrated risk measurement based on the intensity pricing model and Monte Carlo simulations, in which the two main types of risk can be captured simultaneously in the same frame.Secondly, under the framework of the intensity pricing model, this paper proposes a two-factor intensity pricing model for defaultable zero-coupon bonds. We assume a state vector of two independent CIR processes in the real world; also, we assume that the default-free interest rate and the default intensity are affine functions of the state vector such that the two are allowed to be correlated with each other. The affine hypothesis of the model can not only reflect the characteristic of the market variables, but also give a closed-form pricing formula of a defaultable zero-coupon bond and the likelihood function for the parameter estimation. Furthermore, based on the general frame of the integrated risk measurement and the two-factor intensity pricing model, this paper proposes a Monte Carlo Method of calculating integrated-risk VaR for defaultable zero-coupon bonds. We find one loss distribution that reflects the two types of risks in a same risk horizon and one quantile with a same confidence level, so that the integrated-risk VaR can be obtained. The concrete technical detail for Monte Carlo simulations and matlab code are presented, including the simulation of default time and the basic state vector processes.Finally, we estimate the parameters of our two-factor intensity pricing mode using the one-week Shibor and the prices of the Short-term Commercial Paper which is much purer credit corporate bond in our country, and the estimation result indicate that the default-free interest rate is negatively correlated with the default intensity which can be regarded as a sufficient statistic for the credit quality. Moreover, we illustrate the application of our integrated-risk measurement model by computing the integrated-risk VaR of Short-term Commercial Paper, also, we measure the credit risk and the interest risk separately and comparatively analyze the VaR values of the pure interest risk, pure credit risk and integrated-risk.In conclusion,, this paper study the integrated risk measurement model for defaultable zero-coupon bonds considering simultaneously credit risk, market risk and relationship between the two types of risk and measure the total risk in a more comprehensive way. The research can be a preparation for the integrated risk of other types of bonds, risky debts of commercial banks, over-the-counter instruments, credit derivatives and defaultable portfolios and contribute to developing the Enterprise-wide Risk Management.