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?