# A recovery rate of 40 the spread follows from the

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Unformatted text preview: rom the default rate: Pdef 0.00 0.01 0.35 19.19 Price 0.95238 0.95232 0.95038 0.84272 Fixed Income VI: R. J. Hawkins R 5.00 5.01 5.22 18.66 s 0.00 0.01 0.22 13.66 Econ 136: Financial Economics 4/ 22 Risky Debt 300 Value Debt Equity VALUE OF FIRM (USD) 250 Debt (D) is the ﬁrm value less the value of the equity (a call option on the value of the ﬁrm struck at the level of the debt payment B .) 200 150 100 50 0 0 50 100 150 200 250 300 VALUE OF FIRM (USD) The Black-Scholes-Merton equation for the value of the debt is D (V , t ) = V − VN (d1 ) − Be −r (T −t ) N (d2 ) = V [1 − N (d1 )] + Be −r (T −t ) N (d2 ) = VN (−d1 ) + Be −r (T −t ) N (d2 ) Fixed Income VI: R. J. Hawkins Econ 136: Financial Economics 7/ 22 Merton Model of the Credit Spread Representing risk as a yield R : e −Rt = D B Risk as the spread R − r : D = VN (−d1 ) + Be −r (T −t ) N (d2 ) so = Be −r (T −t ) N (d2 ) + B −1 e r (T −t ) VN (−d1 ) D = e −r (T −t ) N (d2 ) + B −1 e r (T −t ) VN (−d1 ) B and R −r = −1 ln N (d2 ) + B −1 e r (T −t ) VN (−d1 ) T...
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## This note was uploaded on 01/23/2014 for the course ECON 136 taught by Professor Szeidl during the Fall '08 term at University of California, Berkeley.

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