Question

The term structure is at with all spot rates equal to 20%. You observe a two-year zero-coupon bond. The first derivative of the bond price with respect to the yield, dP/dy, is -625. What is the price of the bond?

A:$375.00

How to solve this?

Answer 1

Answer.

Let Face value of the bond be "S", Price of the bond is "P"

Yeld to maturity (y)= 20%(given), dP/dy= -625

Time Period(n)= 2 years.

Since the said bond is Zero Coupon Bond so,

Price of Bond = Face value of bond/(1+r)^n

P= S/(1+y)^2 ............. equation 1

P= S* (1+y)^-2

Differentiating both side with respect to "y"

we get,

d/dy (P)= S* d/dy (1+y)-2

dP/dy= S*-2*(1+y)-2-1 (Using formula d /dx(xn)= n*x(n-1) , further noted that "S" be the constant)

dP/dy= -2S/(1+y)^3 ............... equation 2

Now putting the value from above in the said equation 2, we get

-625= -2S/(1+0.20)^3

625= 2S/(1.20)^3

S= (625*(1.20)*(1.20)*(1.20))/2

So, S= $ 540

Putting the value of S and y in equation 1, we get

P= 540/(1+0.20)^2

P= $375

So Price of the bond is $375/-