#1




Value at Risk
Hello all,
Suppose that in the credit default swap market, a CDS contract on bonds issued by company A is trading at 75 basis points. Suppose that a company can sell a 1 million dollar CDS contract and receive 75000 Premium for 5 years [I know 75 basis points and 75000 do not agree with each other but that is what the question states.] each year on January 1st. Suppose that a CDS contract on bonds issued by company B is trading at exactly the same price as that for A. (a) Estimate the probability that the company A defaults during the next year assuming that the CDS is priced in a way that makes the expected profit from selling the CDS as zero, and assuming that default probabilities do not vary during the 5 years. Explain any additional assumptions you make. So how I approached this question was: find an expression for expected profit with a variable 'p' (the probability) and make it equal zero. So it follows: (E)pi = (E)income  (E)Loss = 0 It becomes a Geometric series over the 5 years. So to sum it: SUM [75000*(1(1p)^i)  (1(1p)^i)*1 000 000] = 0 So using the Sum of Geo Series Formula we get: [75000(1p)(1(1p)^i)] / [1(1p)^i] = [1(1p)^i]*1000000 Could someone check this formula to be correct and the resulting solution i achieved: 0.06977 (to 5d.p.) Lastly is that probability a %age? (b) Given your estimate in (a), calculate the 1year 99% VaR for company C that has sold 1 million dollars in CDS coverage on A and also 1million dollars in CDS coverage in company B, assuming that defaults for A and B occur independent of each other, and that C does njot have any other risk positions. This is the one of the two questions I am needing help with. Any help would be greatly appreciated. (c) Assuming that the probability of default in a single year for a company X is 2%, calculate a market price for a 1 million dollar CDS on a company X that is just high enough for company C to sell this CDS (i.e. what is the amount to be paid to the seller for every January 1st.) Anyone able to shed light on these 2 questions would be greatly appreciated. Thank you. 
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