Solutions to Ch5 and Ch6 - KsuWeb

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Problems and Solutions
where R c (t, θ) is the continuously compounded zero-coupon rate at date t with
maturity θ.
On 09/02/02, the model is calibrated, parameters being as follows:
β0 β1 β2 τ1 β3 τ2
5.9% −1.6% −0.5% 5 1% 0.5
At the same date, a manager wants to hedge its bond portfolio P against interestrate
risk. The portfolio contains the following Treasury bonds (delivering annual
coupons, with a $100 face value):
Bond Maturity Coupon Quantity
Bond 1 01/12/05 4 10,000
Bond 2 04/12/06 7.75 10,000
Bond 3 07/12/07 4 10,000
Bond 4 10/12/08 7 10,000
Bond 5 03/12/09 5.75 10,000
Bond 6 10/12/10 5.5 10,000
Bond 7 01/12/12 4 10,000
Bond 8 03/12/15 4.75 10,000
Bond 9 07/12/20 4.5 10,000
Bond 10 01/12/25 5 10,000
Bond 11 07/12/30 4.5 10,000
Bond 12 01/12/31 4 10,000
Bond 13 07/12/32 5 10,000
We consider Treasury bonds as hedging instruments with the following features:
Hedging Asset Coupon Maturity
Hedging Asset 1 4.5 04/15/06
Hedging Asset 2 5 12/28/12
Hedging Asset 3 6 10/05/15
Hedging Asset 4 6 10/10/20
Hedging Asset 5 6.5 10/10/31
Coupons are assumed to be paid annually, and the face value of each bond is $100.
At date t, we force the hedging portfolio to have the opposite value of the portfolio
to be hedged.
1. Compute the price and level, slope and curvature $durations of portfolio P .
2. Compute the price and level, slope and curvature $durations of the five hedging
assets.
3. Which quantities φ1,φ2,φ3, φ4 and φ5 of each hedging asset 1, 2, 3, 4and5do
we have to consider to hedge the portfolio P ?
4. The parameters of the Nelson and Siegel Extended model change instantaneously
to become