Exercise 5. Assume that under the risk-neutral measure Q; the default time is taken

to be an exponential random variable with parameter/intensity ; and is independent

of the interest rate process rt:

i) Compute the zero-coupon bond price with face value 1; maturity T; and recovery-

rate upon default, a positive deterministic constant R; (R

ii) Compute the spread sC of the CDS on the notional amount N; and payment dates

T = f0

in terms of the default-free zero coupon bonds prices.

2

Exercise 5. Assume that under the risk-neutral measure Q, the default time t is taken to be an exponential random variable with parameter/intensity 1, and t is independent of the interest rate process rt. i) Compute the zero-coupon bond price with face value 1, maturity T, and recovery- rate upon default, a positive deterministic constant R, (R