Question 1: Defaultable Bonds and Credit Default Swaps You want to value bonds and credit default swaps of XYZ Widgets. Based on extensive historical data on comparable widget rms, you have determined the risk-neutral survival probabilities. You also observe the term structure of (annually compounded) interest rates.

t 1 2 3 4 5

Risk-neutral survival probability 93.24% 86.94% 81.06% 75.58% 70.47%

Zero-coupon Treasury yields 4% 4.5% 4% 5% 5.5%

1. Suppose that the rm issues a bond paying 6% coupons (annually) with a face value of $1000. The bond is 5 years to maturity. What is the value of this bond? Assume that there is no recovery if the bond defaults.

2. Suppose that the bond in (1) is hard to buy. Instead, you decide to sell protection via a 5-year credit default swap. The CDS will have annual CDS premium payments on a notional amount of $1000. Assume that there is no recovery if the bond defaults. You decide to follow the historical convention of no upfront payment. What is the required CDS premium?

3. If you instead want to structure the contract so that buyers of the insurance have to pay $100 upfront, what CDS premium could you charge?