Assume a = 0.10,b = 0.15,r = 0.04 and σ = 0.35.Using the CIR model,calculate the price of a zero coupon bond maturing in 6 years.

Question

Quizplus · Accepted Answer

Using the CIR model, the price of the zero coupon bond is given by:
P(0,t) = A(t) × exp(-B(t)r(0) )
where:
A(t) = (2a / σ^2)^[2k-1] × [exp^(at)] / [2k-1 + exp^(at)]
B(t) = (2 × k) / [σ^2 × (2k-1 + exp^(at))]
k = sqrt(a^2 + 2σ^2/2) / σ
Substituting the given values, we get:
k = sqrt(0.10^2 + 2 × 0.35^2/2) / 0.35 = 1.930312
A(6) = (2 × 0.10 / 0.35^2)^[2 × 1.930312-1] × [exp^(0.10 × 6)] / [2 × 1.930312-1 + exp^(0.10 × 6)] = 223.8613
B(6) = (2 × 1.930312) / [0.35^2 × (2 × 1.930312-1 + exp^(0.10 × 6))] = 2.0846
Thus, the price of the zero coupon bond is:
P(0,6) = 223.8613 × exp(-2.0846 × 0.04) = 0.7042
Therefore, the best choice is B.