To calculate the theoretical futures price, we need to assume which cheapest-to-deliver (CTD) bond will be delivered by the short counterparty (who will have a choice at maturity of the contract). The quoted price of this CTD bond, which is the underlying commodity in the futures contract, is here assumed to be $115.00. Per the diagram, the quoted CTD bond price is translated into its cash (aka, full) price, by adding the accrued interest (AI). Then we estimate a FORWARD price ($119.711) that corresponds to this spot price ($116.978). Now we just "unravel" this cash forward price (of the CTD bond) by subtracting the anticipated accrued interest ($114.859 is thusly the quote/flat FORWARD price of the CTD bond) and divide by the conversion factor (CF) to obtain the theoretical FUTURES price: $1114.859 divided by 1.60 = $71.787.
David's XLS is here: https://www.dropbox.com/scl/fi/gdutpwu4895th082aqmu0/082718-tbond-futures-price.xlsx
David's XLS is here: https://www.dropbox.com/scl/fi/gdutpwu4895th082aqmu0/082718-tbond-futures-price.xlsx
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