This section addresses the equivalence between credit spreads and default probabilities under risk-neutrality. Risk-neutrality means that investors are indifferent between the expected value of a random flow and the certain flow having a value equal to the expected value of the random one. Since this is unrealistic, natural or real probabilities differ from risk-neutral probabilities. […]
Natural default probabilities are the actual ones. If we use the observed historical probability of default of 1.5%, the expected value of the random unit flow of the risky debt is: This future value is above 1.06, that of the risk-free debt. There is no reason to expect that the values will coincide if we […]
The risk-neutral default probability is such that the risky debt expected value at the horizon is equal to that of the risk-free debt. The risk-neutral probability from 0 to n is d*(0, n), instead of d(0, n), the natural default probability. It is such that: This risk-neutral default probability is higher than the observed default […]
Full valuation mixes several effects. First, it combines the risk effect with the relative richness or poorness effect, or the influence of the excess spread of an asset over the market required yields. Second, a longer maturity increases the length of exposure to credit risk. Third, the effect of a longer maturity on value depends […]
Under risk-neutral valuation, risk-free rates apply to the expected flows calculated with risk-neutral probabilities. KMV Portfolio Manager provides credit spread valuation and is the only model also providing risk-neutral valuation by modelling risk-neutral probabilities directly. For each expected default frequency Edf, there is a risk-neutral probability embedding the effect of risk aversion.
The basic economic measures of risk are the Expected Loss (EL), the standalone Loss Volatility (LV) and the Value at Risk (VaR). The EL serves for economic provisioning, and for statistical loss management, while the LV captures the dispersion of losses around the mean and relates to the unexpected loss concept. VaR measures define capital […]
This section details the loss distribution relative to a single standalone banking exposure. The subsections address the same issues using a simple portfolio of two exposures only. FULL VALUATION OF MIGRATION RISK Under full valuation mode, there are as many values as there are migration states, plus the default state. A single facility has a […]
The risk of traded instruments exists over the holding period only. The hold to maturity view does not hold because it is possible to get rid of the exposure whenever a warning light turns on. The view on credit risk for such an exposure is that it is the specific risk of value variations unrelated […]
Specific Risk for Bonds and Credit Risk VaR Credit risk models address the issue for bond portfolios as for loans. The horizon is a parameter controlled by the banks. Generally, banks measure credit risk with portfolio models on their loans over a horizon of at least 1 year, because of the hold to maturity philosophy. […]
The correlation building blocks of models capture the obligors credit risk correlation across borrowers and/or with external factors. This is a critical modelling block because: the correlations of credit risks are positive, increasing the risk of losses; they drive the shape of loss distributions and generate fat tails highly sensitive to correlations; they relate to […]
