Problem 3: Credit Default Swap and Reinsurance

A hedge fund invests in a corporate bond with a face value of $1000, semi-annual coupons of %10 and time to maturity of 1 year. The bond is currently trading at par.

a. What are the payoffs to the bondholder.

b. Compute the value of the bond at t=0.5, right after the first coupon is paid? (Hint: first compute the YTM)

c. What is the forward price of the bond, today, for delivery t=0.6?

With 25% probability, the bond defaults at t=12/12, so that the bondholder does not receive the face value and the coupon at t=12/12 with such a probability. To hedge the risk, the hedge fund enters a CDS with a bank. In the operation, each time the bond does not default, the hedge fund pays a premium P to the bank. In the event of a default, the hedge fund does not pay a premium, but instead receives the face value from the bank ($1,000). Assume that the CCIR is 5%

d. What is the PV of cash flows that the bank expects to receive? To give? (This should be a function of P)

e. What is the premium that the bank will charge the hedge fund?

f. Now, with 40% the hedge fund is liquidated at t=12/12. If liquidated, the bank does not receive the payment P. What is the premium that the bank will charge the hedge fund?

Let's go back to the setting for question d) and e). After entering the CDS with the hedge fund at t=0, the bank wants to hedge itself from the risk of the CDS. So, it enters a CDS on a CDS (i.e., reinsurance) For convenience, assume that Bank A is the bank that enters the CDS with the hedge fund (question d) and e)). And that Bank A now enters a CDS with Bank B. That is, Bank A will pay Bank B an amount R every time Bank A receives the payment P. If not, Bank A will receive from Bank B an amount equal to 1000.

g. What is the value or R?