Notes_12_finance_5108_08

Notes_12_finance_5108_08 - Finance 5108 Notes 12 Credit...

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Finance 5108 Notes 12 Credit Risk and Credit Derivatives Learning objectives 1. Understand ratings and the system of rating for bonds 2. Understand and be able to use historical information on defaults and recoveries 3. Probabilities of default and bond risk premiums and their use 4. Understand the difference between historical estimates and implied probabilities from bond prices 5. The use of stock prices to estimate default probabilities using option pricing models 6. Understand credit risk in derivative transaction and how credit risk can be mitigated 7. The effects of correlation on default estimates and the time to default calculations 8. Credit Value at Risk 9. Credit default swaps their structure and valuation 10 CDO (Collateralized Debt Obligations) Structure and valuation 11.Covertible Bonds and Their evaluation Rating Rating are estimates of the credit worthiness of a borrower done by an independent credit rating agency. 1. S&P AAA to CCC 2. Moody’s Aaa to Caa 3. Fitches AAA to CCC Historical Defaults Terms 1. An unconditional default probability is the probability of a bond defaulting in a given year. 2. Conditional Default probabilities (also called default intensities or hazard rates) are the probability of default in a given year conditional on no earlier defaults The average default intensity between time 0 to time t is - (t) t Q(t) = 1-e where (t) is the default intensity at time t λ The historical recovery rate is presented in table 20.2 The relationship between recovery rates and default rate was found by moddy’s to be
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Average recovery rate = 50.3-6.3 X average default rate. These are measured in percent. Calculating the default probabilities using bond prices Following procedure 1. Calculate the present value of the expected default rate as a function of the default probability 2. Set this equal to the value of the default risk premium Example 20.15 Risk free rate is 3.5% continuous compounding 3 year and 5 year bonds with a 4.5% and 4.75% annual pay coupons Recovery rate 40% Default can only occur mid year Default Risk- free PVIF PV E(loss) 0.5 Q 40 103.01 63.013 0.9827 61.919865 1.5 Q 40 102.61 62.611 0.9489 59.408718 2.5 Q 40 102.2 62.195 0.9162 56.984233 178.31282 0.5 Q 40 104.14 64.136 0.9827 63.023089 1.5 Q 40 103.4 63.4 0.9489 60.157554 2.5 Q 40 103.01 63.013 0.9162 57.733425 3.5 Q 40 102.61 62.611 0.8847 55.392675 4.5 Q 40 102.2 62.196 0.8543 53.13243 289.43917 Value of the Bond = 98.346131 Value of the risk-free Bond = 101.22665 Difference = 101.225665- 98.346131 = 2.879534 So 178.3128Q = 2.85934 Q = .016149 or 1.6149% Value of the bond = 96.242682 Value of the Risk Free Bond = 101.974125 Difference 101.94125-96.24682 = 5.727305 289.4392Q = 5.727305 = .019788 or 1.9788% (1-.016149) 3 *(1-X) 2 = (1-.019788) 5 or X = .02522 or 2.522%
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Risk free rate sometimes taken as the libor/swap rate zero fro default probability calculations Asset Swaps Asset swap spread are used to extract default probabilities For instance if the asset default swap rate is 100 basis point in the first part
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This note was uploaded on 11/23/2009 for the course FIN 5180 taught by Professor Rader during the Fall '09 term at Temple.

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Notes_12_finance_5108_08 - Finance 5108 Notes 12 Credit...

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