Would anyone have a practical example of how/where this conversion factor comes from?
I think I understand that to arrive at the future price that the long party has to pay, we just multiply the “future price * conversion factor”.

My understanding is that we use this conversion factor because there’s an optionality for the short party in choosing the bond to deliver, but I have no idea really what this means. Any clarification would be super helpful as I really want to understand it. E.g., that a bond has 0.8??

The theoretical bond underlying the US T-bond futures contract is a 20-year, 6% coupon, option-free bond.

The problem is that no such bond exists.

Therefore, the short is allowed to deliver any T-bond with at least 15 years to maturity or first call.

The problem is, none of those bonds will be trading at the same price as the theoretical bond.

Therefore, to try to ensure that the long gets full value when the contract expires, each eligible bond is given a conversion factor, which is calculated as its price divided by the theoretical bond’s price. That conversion factor is then applied to the par amount of that bond that must be delivered.

For US T-bond futures, the contract size is USD 100,000 par. If bond A has a conversion factor of, say, 1.2000, then short would have to deliver to long USD 120,000 (= USD 100,000 × 1.2000) par of bond A.