Question

Consider a $1000 face value risk-free 1-year zero coupon with an interest rate of 5%. Consider a 1-year zero-coupon bond with the following risky cash flows:

Payoffs = $1,000 with prob .90 700 with prob .10

The discount rate of the risky bond is 6%. Answer the following questions:

a. What is the price of the risk free bond?

b. What is the price of the risky bond?

c. Suppose there is a CDS completely hedging away the default risk of the risky bond. What is its price?

d. What would be the price of the CDS when the bond does not have any systematic risk? Why the CDS price is cheaper than the one in C?

Answer 1

Answer :

a. Price of Risk free Bond = Payoff / ( 1 + risk free Interest rate ) = $ 1000 / ( 1+ 5%) = $ 952.38

b. Price of the risky bond = Payoff / ( 1 + risky Interest rate ) = $ ( 0.90 x 900 + 0.10 x 100 ) / ( 1+ 6%) = $ 970 / ( 1 + 6% )

= $ 915.09

c. Suppose there is a CDS completely hedging away the default risk of the risky bond , then it's price be

= $ 952.38 - $ 915.09 = $ 37.28

d. The price of the CDS when the bond does not have any systematic risk would be

First we need to calculate price of a bond at risk free return with risky payoff = $ 970 / ( 1+5%) = $ 923.80

Then , we calculate the amount of systematic risk = $ 923.80 - $ 915.09 = $ 8.71

we eliminate the systematic risk from CDS in part C = $ 37.28 - $ 8.71 = $ 28.57

The CDS price is cheaper than the one in C because there is systematic risk of 1% which is interest risk , but if in current scenario the cash flows are vary as per risk then in such case the interest risk should be eliminated to calculate the CDS price