Question

It is march 10, 2020. the cheapest-to-deliver bond in a december 2020 treasury bond futures contract is an 8% coupon bond, and delivery is expected to be made on december 31, 2020. coupon payments on the bond are made on march 1 and september 1 each year. the rate of interest with continuous compounding is 5% per annum for all maturities. the conversion factor for the bond is 1.2191. the current quoted bond price is $137. calculate the cash bond price, cash futures price, and quoted futures price for the contract. 12

Answer 1

To calculate the cash bond price, discount future cash flows. Cash futures price equals cash bond price multiplied by the conversion factor. Quoted futures price equals cash futures price divided by the conversion factor.

Step-by-step explanation:

To calculate the cash bond price, we need to discount the future cash flows of the bond to their present value.

The cash bond price is the sum of the present values of the coupon payments and the face value of the bond.

Here’s how to calculate it:

1. Calculate the present value of each coupon payment using the continuous compounding interest rate of 5% and the time to each coupon payment.
2. Calculate the present value of the face value using the continuous compounding interest rate of 5% and the time to maturity.
3. Add up the present values of the coupon payments and the present value of the face value to get the cash bond price.

The cash futures price is the cash bond price adjusted for the conversion factor. Here’s how to calculate it:

1. Multiply the cash bond price by the conversion factor to get the cash futures price.

The quoted futures price for the contract is the cash futures price divided by the conversion factor. Here’s how to calculate it:

1. Divide the cash futures price by the conversion factor to get the quoted futures price.