The Market Price of Credit Risk

1 The Ma rk et Price of Credit Risk Ka y Giesecke Cornell University giesecke@orie.cornell.edu www.orie.cornell.edu/ s giesecke Lisa R. Goldberg lrg@barra.com The Market Price of Credit Risk 2 We live in a dangerous world † Issuers of default able securities share a common dependence on the economic environment † Aggregate credit risk cannot be diversified away † Undiversified able o r systematic risk commands a p remium { Risk-averse investors must b e compensated for assuming systematic credit risk † The credit premium is empirically w ell-documented, and theoretically complex { Why is it important to understand it?

The Ma rk et Price of Credit Risk 3 Ho w is a credit mo del used? † T o fo recast the actual p robabilit y of default { Mo del must re ect histo rical default exp erience { Actual lik eliho o d of default † T o estimate the value of default sensitive securities { Mo del must flt ma rk et p rices { Ma rk et-implied lik eliho o d of default Actual Likelihood of Default Market-implied Likelihood of Default Credit Risk Premium The Market Price of Credit Risk 4 What’s the difference? Risk less bond Default able bond R(1)=10R(0)=10 t=0 t=1 D(1)=20 if no default D(0)=5 D(1)=0 if default p=0.5 Actual likelihood of default p=0.5 (coin flip) 1-p Market-implied likelihood of default q=0.75 1-q q The Market Price of Credit Risk 5 First passage structural credit model † Default occurs when firm value X falls below a barrier D : ¿ = inf f t > 0 : X t • D g † Requires { A model of firm value process X { A model of default barrier D † Identifies equity as a down-and-out call option on the firm † Default probability given b y the distribution of min s• T X s The Market Price of Credit Risk 6 First passage structural credit model D Default No Default Default Probability τ τ τ T X Density of minimum of X The Market Price of Credit Risk 7 First passage credit risk premium † Credit risk is exclusively driven b y uncertainty ab out firm value † Risk premium takes a familiar fo rm (X a („; )-GBM) { Excess return on credit sensitive security is equal to its
isk" times the market p rice of that risk { Risk is measured in terms of difiusive price volatility { The market p rice of risk is given b y „ ¡ r ; the excess return „ ¡ r on the firm p er unit of firm risk The Market Price of Credit Risk 8 Caveats This simple representation of the risk premium neglects the short-term uncertainty surrounding the default † Distance...

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