Short rates follow a Cox-Ingersoll-Ross model.
A market maker purchases a zero coupon bond maturing in 5 years and delta-hedges it by selling k zero coupon bonds maturing in one year. You are given:
(i) when r=.06, k=2.12091
(ii) when r=.08, k=2.06739
Determine k when r =.03.
In the solution we use:
k= (P(r,0,5)*B(0,5))/(P(r,0,1)*B(0,1)) =
[ A(0,5)B(0,5)e^-B(0,5)r] / [ A(0,1)B(0,1)e^-B(0,1)r]
which I understand. However, next the jump to
=(k_1)*e^(r*(k_2) )
How is this jump made?
A market maker purchases a zero coupon bond maturing in 5 years and delta-hedges it by selling k zero coupon bonds maturing in one year. You are given:
(i) when r=.06, k=2.12091
(ii) when r=.08, k=2.06739
Determine k when r =.03.
In the solution we use:
k= (P(r,0,5)*B(0,5))/(P(r,0,1)*B(0,1)) =
[ A(0,5)B(0,5)e^-B(0,5)r] / [ A(0,1)B(0,1)e^-B(0,1)r]
which I understand. However, next the jump to
=(k_1)*e^(r*(k_2) )
How is this jump made?
ASM Manual question 26.33
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