Bond risk. Consider a 4% coupon bond with 6 months to maturity and a par value of $100. Assume that from the ZCB prices, we nd that the market's 6 month spot rate is r.5 = .003.

(a) What is the price of this bond if there is no default risk?

(b) What is the yield?

(c) Now, consider a more realistic scenario in which there is a 90% probability that the bond makes all of its obligatory payments and a 10% chance that it defaults. From an internal model, we ascertain that if this company defaults we will be able to only recoup 30% of the par value (and no coupons). What is the fair-market price now?

(d) What financial instrument, if we can find it in the market, would allow us to hedge this default risk? What would this agreement between us and the issuer look like?