m48-ch26 - Chapter 26 Credit Risk Question 26.1. Using...

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Chapter 26 Credit Risk Question 26.1. Using formulas in the main text book, we can calculate the true and risk-neutral probability of bankruptcy to be 0.4256 and 0.5808, respectively. To calculate the credit spread, we need to know the expected loss given default, which is one less the expected recovery rate. We can calculate for the risk-neutral probability measure an expected asset value conditional of default of 62.9118, and an expected recovery rate of 0.5243 (don’t forget to divide by 120—the maturity value, and NOT by 100). Using the last formula to calculate the credit spread, we obtain a credit spread of 6.467%. Question 26.2. Using the formulas of the main text, we can calculate the following values for the yield, the probability of default, and the expected loss given default for all times to maturity: Years to Yield Prob Default Recovery Expected Loss Approx Maturity Given Default 1 0.215502281 0.5 74.65543 0.253445658 0.206723 2 0.169925969 0.5 67.07878 0.329212215 0.162303 3 0.150053883 0.5 62.09065 0.379093545 0.143182 4 0.138376782 0.5 58.35039 0.416496097 0.132062 5 0.130513667 0.5 55.36063 0.446393746 0.124639 10 0.111591282 0.5 45.8246 0.541753977 0.107088 20 0.099109428 0.5 36.47327 0.63526726 0.095882 Note that the probability of default is constant for the parameter values chosen. The last column of the above table shows the approximations. They work remarkably well. Question 26.3. Given the information in the text, we can calculate: mat val 110 time to mat 3 Bond price 67.46671139 yield 0.162948685 prob default 0.554709232 Expected 66.31404877 recovery 323
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Part 5 Advanced Pricing Theory Equation 26.5 states that ρ r = 1 T ln · 1 1 prob * ( default ) × E ( Loss given default ) ¸ We can use the equation above to calculate a yield from the probability of default and the expected loss given default. The expected loss given default is equal to 66 . 31405 / 110 = 0 . 397145. We can calculate: ρ = 0 . 08 + 1 3 ln · 1 1 0 . 5547 × 0 . 3971 ¸ = 0 . 162948685 This is equivalent to the yield we calculated above, which was to be shown. Question 26.4. a) We can calculate for a maturity value of $80 mat val 80 80 80 80 80 80 80 T i m e t o m a t 12345 1 0 2 0 Bond price 69.453 61.391 54.921 49.458 44.728 27.965 11.661 Yield 0.141 0.132 0.125 0.120 0.116 0.105 0.096 Prob default 0.288 0.347 0.374 0.390 0.401 0.430 0.450 Expected recovery 63.489 57.044 52.754 49.526 46.940 38.688 30.614 Expected loss given default 0.206 0.287 0.341 0.381 0.413 0.516 0.617 b) For a maturity value of $120, we obtain: mat val 120 120 120 120 120 120 120 T i m e t o m a t 1 0 2 0 Bond price 88.145 78.590 70.773 64.077 58.214 36.989 15.711 Yield 0.309 0.212 0.176 0.157 0.145 0.118 0.102 Prob default 0.676 0.626 0.604 0.590 0.581 0.557 0.541 Expected recovery 83.723 75.660 70.264 66.186 62.912 52.390 41.971 Expected loss given default 0.302 0.369 0.414 0.448 0.476 0.563 0.650 c) For a maturity value of $80, the probability of default is increasing, and for a maturity value of $120, the probability of default is decreasing. If the maturity value is $80, we start out with a bond obligation that is well below our current asset threshold. Within a short time to maturity it is more unlikely that the asset value decreases below the threshold of $80, but the likelihood increases with time to maturity. Conversely, with a maturity value of $120, we have a debt obligation that is considerably higher than our current asset value. The initial probability of default is very high. The
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This note was uploaded on 12/06/2011 for the course ECON 101 taught by Professor Adam during the Spring '06 term at Neumann.

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m48-ch26 - Chapter 26 Credit Risk Question 26.1. Using...

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