An Integrative Risk Evaluation Model for Market Risk and Credit Risk

Not only financial institutions but all firms have their own portfolio consisting of various financial assets. These portfolios are exposed to many kinds of risks, such as market risk, credit risk, liquidity risk, operational risk, and so on. Basel Accord in 1998 prompted us to recognize the importance of quantitatively evaluating these financial risks, and risk valuation models have been developed, first for market risk and then credit risk. However, in these models, each risk is evaluated separately, not integratively. Recently, Kijima and Muromachi [17] proposed a general framework for the integrative evaluation of market risk (interest rate risk) and credit risk. In this paper, we extend Kijima and Muromachi [17], and propose a framework to evaluate in a integrative way market risk (not only interest rate risk but also stock price variation risk and foreign exchange risk) and credit risk. At the center of the framework are stochastic differential equations (SDEs) which describe the dynamics of interest rate and default probability. We (i) run simulations with in the MonteCarlo method and generate scenarios based on these basic equations, (ii) calculate asset values for a pre-specified future date (risk horizon) using no-arbitrage theory, and (iii) obtain the future value of the portfolio by summing up all asset values. The main features of this framework are: (i) we can take the correlation between the interest rate and the default probability into account, (ii) the theoretical values of bonds derived in this setting are consistent with those observed in the real market, (iii) we can incorporate the term structure of the default probability into the model. Moreover, we can obtain the distribution of the portfolio or each asset value in the future, and so we can calculate any risk measure (e.g. standard deviation, VaR, T-VaR etc.). Also, the expected return can be computed, so the risk-return analysis can be made in a consistent way. This framework enables us to construct many types of models by changing the basic SDEs. We briefly present results for a Gaussian model, which is relatively easy to calculate.