Question

Question 8: Find a 9-month forward price for a 9% coupon bond that matures 28 month from now if short-term interest rate (for any time period under 1 year) is 10% and the current bond price is equal to $92 Ans: Next coupon is in 4 month. Hence, I=4.5*exp(-0.1*4/12). Therefore, F=(92-4.5*exp(-0.144/12) *exp(0.1*9/12)=$94.47 Give 0.5 points if the answer is F=(92-4.5)*exp(0.1*9/12)=$94.31

where has the number come from?

I need an explanation for the formula.

Answer 1

Solution:

The formula used in the question has two part -

1. Finding the present value of coupon payment

2. Finding the forward price using the spot price

Question 8 )

The coupon rate is 9% annual that means 4.5% semi annual.

The bond has maturity in 28 months that means the next coupon payment will be in 4 months ( 24 + 4 months ) .

Let's find the present value of this future coupon payment of 4.5.

I = coupon * exp ( - interest rate * time )

I = 4.5 * exp ( -0.1* 4/12) {time is 4/12 because next coupon payment is in 4 months

Forward price = ( Current price - present value of future income ) * exp ( interest rate * time of forward )

F = (92- 4.5 * exp( -0.1*4/12) )* exp (0.1 * 9/12) = 94.47

Question 5 )

Similar as question 8, here coupon payment is in 2 months as bond has maturity of 7 years and 8 months and coupon payment is semiannually.

Forward is for 5 months hence time for forward = 5 months