Question 2: Hedging Corporate Bonds with CDS

Urban Meyer Sports Inc. has issued a zero-coupon corporate bond that matures in 1 year. It has a face value of $1000. You estimate the risk-neutral survival probability of Urban Meyer Sports to be 97%. Assume that the recovery rate is 40% if default occurs.

In addition, you observe that a zero-coupon one-year Treasury bond with a face value of $1000 is trading at $952.38.

1. What should the price of the Urban Meyer Sports bond be?

2. Suppose that there is a one-year CDS contract trading on Urban Meyer Sports. Sup-pose that this contract has no periodic premium payment. Thus, the only payment for this insurance is through an upfront payment. What is the fair upfront payment?

3. Suppose that the upfront payment for the one-year CDS described in (2) is instead $10. Construct an arbitrage trading strategy using the Urban Meyer Sports Inc bond, the Treasury bond, and the CDS to take advantage of this mispricing. Show the cashows to your portfolio (i) today, (ii) next year if the Urban Meyer bond defaults, and (iii) next year if the Urban Meyer bond does not default.

4. Suppose the contract in (2) required an annual CDS premium (as in traditional CDS contracts) rather than an upfront payment. What would the fair premium be? Convert the premium to dollars. What are two reasons that this amount is dierent from the amount in (2)?