PLEASE WRITE ALL THE FORMULAS AND CALCULATIONS

Question 2 [10 points]

Consider a 10% two year corporate bond. This bond pays a coupon of $10 at t=1 and pays back $110 at t=2. The default spread for an AAA rated bond is 0.25% and a BB rated bond is 9%. Suppose the risk free rate is constant at 1%.

1. (a) Suppose the bond has an AAA rating. What is the market price of the bond at t=0?

   [3p]

2. (b) Suppose the bond has a BB rating. Do investors buy the bond for $100 at t=0? [3p]

Suppose the central bank changes the interest rate. Please comment on the following statements. (You can use a numerical example to illustrate your answer.)

(c) The price of the AAA rated bond goes up, if the central bank increases the risk free interest rate. [2p]

(d) If the yield curve is not constant but increasing, the price of the BB rated bond goes up ceteris paribus. [2p]