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Unformatted text preview: III. Managing NonMarket Risks A. Credit Risk Introduction o One of the oldest risks o Credit risk is the potential for loss due to nonpayment of any amounts owed . The expected loss is given as follows: n Expected loss = [probability of default] times [amount owed] times [percentage of amount owed not paid] Version: January 3, 2011 p. 2 of 53 Unit III.A Introduction (cont.) A bank makes a $1,000 loan to a company. The bank believes there is a 90% chance the company will pay back the full $1,000 and a 10% chance the company will default. If the company defaults, the bank expects to recover $200. The expected loss can be derived several ways. The expected payback is $1,000(0.9) + $200(0.1) = $920. Thus, the expected loss is $80. Alternatively, the probability of default is 0.1, the amount owed is $1,000, and the percentage of the amount owed not paid is 80%. Multiplying these we obtain $1,000(0.1)(0.8) = $80 Version: January 3, 2011 p. 3 of 53 Unit III.A Introduction (cont.) o A 2% probability of default amounts to a much higher probability of default over a longer period. For ten years, n 1 – (0.98)10 = 0.1829. o Default does not necessarily mean 100% loss. There is a recovery rate. o We must define a credit event . o Credit rating agencies play a big role. Version: January 3, 2011 p. 4 of 53 Unit III.A Credit Risk as an Option Consider a company that has assets today worth A0. It has one issue of zero coupon debt due at time T with face value of F. At time T, if the assets exceed the value of the debt, the company will pay off the debt and the stockholders will get the remainder. If not, the company will default, giving the creditors whatever assets it has. The stockholders’ personal assets cannot be claimed by the creditors. Let us look at what happens at T: Payoff at Time T AT ≤ F AT > F Bond AT F Stock AT – F Total paid to suppliers of capital AT AT Version: January 3, 2011 p. 5 of 53 Unit III.A Credit Risk as an Option (cont.) The stock behaves like a call so we can price it using BlackScholesMerton. The BlackScholesMerton formula isrT 1 2 2 1 2 1 C = S N(d )  Xe N(d ) ln(S / X) + (r + (σ / 2))T d = σ T d = d σ T. Version: January 3, 2011 p. 6 of 53 Unit III.A Credit Risk as an Option (cont.)rT 1 2 2 1 2 2 1 S = A N(d ) Fe N(d ) ln(A / X) + (r + (σ / 2))T x = σ T ln(A / X) + (r (σ / 2))T x = = xσ T σ T The current market value of the assets is A0, and the current market value of the stock is S0. Therefore, by definition, the market value of the bonds is B0 = A0 – S0. Version: January 3, 2011 p. 7 of 53 Unit III.A Credit Risk as an Option (cont.) So rewrite putcall parity in the context of this problem as P0 + A0 = S0 + F(1 + r)T....
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 Fall '11
 DonChance
 Collateralized debt obligation, Credit default swap, Credit derivative

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