You have a discount bond with a time to maturity of one year. The market price of this instrument is 97%. You want the model price to match it while you build you yield curve with ED futures; the contracts price as follows: 1st = 99, 2nd = 98, 4th =97. What is the price of the third contract?
To determine the price of the third contract, we can use the concept of interpolation. Since we know the prices of the first, second, and fourth contracts, we can interpolate the price of the third contract based on these values.
Interpolation is a common method used to estimate values between two known values. In this case, we will use linear interpolation.
First, let's arrange the given contract prices in ascending order:
1st contract = 99
2nd contract = 98
4th contract = 97
Now, let's calculate the price of the third contract using linear interpolation:
Step 1: Calculate the difference between the prices of the fourth and second contract:
difference = 97 - 98 = -1
Step 2: Divide the difference by the difference between the contract numbers:
price difference per contract = difference / (4 - 2) = -1 / 2 = -0.5
Step 3: Determine the difference between the third contract and the second contract:
third contract difference = 3 - 2 = 1
Step 4: Multiply the third contract difference by the price difference per contract:
interpolated price = second contract price + (third contract difference * price difference per contract)
interpolated price = 98 + (1 * -0.5) = 97.5
Therefore, the price of the third contract is 97.5.