Question

Current 1-year spot rate is 3.5%. Annual volatility of interest

rates is 10%. If r1 (low) =4.5%, calculate the price of a 2-year
bond with annual 3% coupon (paid annually). Assume face value of
$100.

Answer 1

To find the bond price, we discount each of the bond's future cash flows back to the present using the respective interest rates for their time to maturities. The sum of these discounted cash flows gives us the bond's price.

Step-by-step explanation:

To calculate the price of the 2-year bond with a 3% coupon and a face value of $100, we need to discount its future payments by the current 1-year spot rate of 3.5%. Since the first coupon payment occurs in 1 year, it is discounted by the 1-year spot rate.

The second coupon payment, which includes both the coupon and the face value, occurs in 2 years and is discounted by r1 (low) which is given as 4.5%. This predicament arises because the second year's rate is different from the first year, which has to be calculated separately as a forward rate. However, for the sake of the example, we will use the provided 4.5% rate without deriving the forward rate which usually requires additional calculations.