Solutions to Ch5 and Ch6 - KsuWeb

Problems and Solutions
On 09/02/02, the values of the Nelson and Siegel Extended parameters are as
follows:
β0 β1 β2 τ1 β3 τ2
5.9% −1.6% −0.5% 5 1% 0.5
Recall from Chapter 4 that the continuously compounded zero-coupon rate
Rc (0,θ) is given by the following formula:
R c ⎡
1 − exp −
(0,θ)= β0 + β1 ⎣ θ ⎤
τ1 ⎦
+ β2
+ β3
θ
τ1
⎡
1 − exp −
⎣ θ
τ1
θ
τ1
⎡
1 − exp −
⎣ θ
τ2
θ
τ2
− exp − θ
τ1
⎤
⎦
− exp − θ
τ2
⎤
⎦
1. Draw the zero-coupon yield curve associated with this set of parameters.
2. We consider three bonds with the following features. Coupon frequency is
annual.
Maturity Coupon
(years) (%)
Bond 1 3 4
Bond 2 7 5
Bond 3 15 6
Compute the price and the level, slope and curvature $durations of each bond.
Compute also the same $durations for a portfolio with 100 units of Bond 1, 200
units of Bond 2 and 100 units of Bond 3.
3. The parameters of the Nelson and Siegel Extended model change instantaneously
to become
β0 β1 β2 τ1 β3 τ2
5.5% −1% 0.1% 5 2% 0.5
(a) Draw the new zero-coupon yield curve.
(b) Compute the new price of the bond portfolio and compare it with the value
given by the following equation:
New Estimated Price = Former Price + β0.D0,P + β1.D1,P
+ β2.D2,P + β3.D3,P
where βi is the change in value of parameter βi, andDi,P is the $duration
of the bond portfolio associated with parameter βi.
4. Same questions when the coupon frequency is semiannual.
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