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Old 03-23-2011, 09:11 PM
laauu laauu is offline
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Join Date: Mar 2011
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Default 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-(1-p)^i) - (1-(1-p)^i)*1 000 000] = 0

So using the Sum of Geo Series Formula we get:

[75000(1-p)(1-(1-p)^i)] / [1-(1-p)^i] = [1-(1-p)^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 1-year 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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