Question One
You have been asked to price a one year CDS contract. You are given the following information.
Notional $10 mm.
Recovery rate 0.35
Table
LIBOR Term Structure Hazard Function
Maturity,
Years Z(0, T) Maturity, Years Hazard
0.25 0.997503 0.25 0.0600
0.50 0.995012 0.50 0.0598
0.75 0.992528 0.75 0.0590
1.00 0.990050 1.00 0.0585
(a) Determine the term structure of survival probabilities
(b) Determine the present value of the premium payments, assuming the spread is one.
(c) Determine the present value of the protection leg.
(d) What is the CDS spread?
(e) If the CDS spread was 100 basis points, what is the value of the CDS to the protection buyer?
Question Two
The LIBOR term structure of interest rates is generated by Z(0, t) = exp( - L * t), where L = 0.02. The term structure of survival probabilities is generated by Q(0, t) = exp( - λ * t), where λ= 0.02. The recovery rate is 0.40. We want to price a five year CDS.
1. Determine the term structure of survival probabilities.
2. Determine the present value of the premium payments, assuming the spread is one.
3. Determine the present value of the protection leg.
4. What is the CDS spread?
5. If the spread is fixed at 100 basis points, what is the up-front fee?
6. How does the spread vary (there is no up-front fee) as (a) the hazard rate λ = 0.02, 0.04, 0.06 and if the recovery rate varies between R = 0.30, 0.35, 0.40, 45, 0.50? Comment on your results.