91Ó°ÊÓ

Suppose that the risk-free zero curve is flat at \(7 \%\) per annum with continuous compounding and that defaults can occur halfway through each year in a new 5 -year credit default swap. Suppose that the recovery rate is \(30 \%\) and the default probabilities each year conditional on no earlier default is \(3 \%\). Estimate the credit default swap spread. Assume payments are made annually.

How does a 5 -year \(n\) th-to-default credit default swap work? Consider a basket of 100 reference entities where each reference entity has a probability of defaulting in each year of \(1 \%\). As the default correlation between the reference entities increases what would you expect to happen to the value of the swap when (a) \(n=1\) and (b) \(n=25\). Explain your answer.

How does a 5-year nth-to-default credit default swap work? Consider a basket of 100 reference entities where each reference entity has a probability of defaulting in each year of \(1 \%\). As the default correlation between the reference entities increases what would you expect to happen to the value of the swap when (a) \(n=1\) and (b) \(n=25\). Explain your answer.

What is the formula relating the payoff on a CDS to the notional principal and the recovery rate?

Show that the spread for a new plain vanilla CDS should be \((1-R)\) times the spread for a similar new binary CDS. where \(R\) is the recovery rate.

A company enters into a total return swap where it receives the return on a corporate bond paying a coupon of \(5 \%\) and pays LIBOR. Explain the difference between this and a regular swap where \(5 \%\) is exchanged for LIBOR.

$$ \text { Explain how forward contracts and options on credit default swaps are structured. } $$

"The position of a buyer of a credit default swap is similar to the position of someone who is long a risk-free bond and short a corporate bond." Explain this statement.

Why is there a potential asymmetric information problem in credit default swaps?

$$ \text { Why is there a potential asymmetric information problem in credit default swaps? } $$