In: Finance
In January 2020, the term-structure of spot rates is as follows (with continuous compounding):
Maturity (years) Zero-rate(%)
1 2.0
2 3.0
3 4.0
A 3-year zero-coupon bond has the face value of $1,000. Consider a 1-year forward contract on the zero coupon bond. What should be the forward price?
(a) $904.84 (b) $923.12 (c) $941.77 (d) $960.79
Present value = Future value / e^n*r
n = number if periods
r = rate of interest
Step - 1:
First let's calculate spot value (i.e., at year 0)
Present value = 1000 / e^3*4%
= 1000 * 0.88692
Spot value = $886.92
Step - 2:
Future value = Present value * e^r*n
Value after one year = 886.92*e^1*2%
= 886.92 * 1.02020134
So forward rate = $904.84
Option a is correct