Measuring Default Risk from Market Prices Following P. Jorion, Financial Risk Management Chapter 20
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Credit losses can be forecast from credit rating and historical default rates and recovery rates Content Infer default risk for bonds Merton's model (Structural Model)
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Corporate Bond Prices Spread and Default Risk Assume thee bond makes only one payment of $100 in one period, yield can be computed from price:
can be compared to the risk free rate over the same period Risk neutral valuation
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Risk Neutral Valuation
The credit spread = Probability of Default * Loss Given Default
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Example
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Multi Periods
Recovering the term structure of forward default probabilities Daniel HERLEMONT
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Risk Premium The risk neutral probabiliy is not the same as the objective (or historical) probabilities π'
The investor requires some compensation for bearing credit risk
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The Cross Section of Yield Spread
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Equity Prices The credit Spread approach is only valid when there is a "good" bond market data. This is rarely the cas: Many countries don't have a well developed corporate bond market The counterparty may not have an outstanding publicy traded bond or if os they contain optional clauses (such as call) The bond may not be traded actively use other source of data such as Equity prices Daniel HERLEMONT
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Merton's Model Merton 1974 V(t)=value of the firm at time t K= face value of the corporate zero coupon bond, maturity T
Equity price can be viewed as a call on the value of the firm
Bond
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Stock Valuation
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Bond Valuation
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KMV approach Many advantages: rely on equity prices (much more liquid) rather than bond prices correlations between equity prices can be used to assess correlation between default Link Estimated Default Frequency with rating
