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What is the difference between

1) computing the 'forward price' of a bond at a future time T. ( spot price - carry, involving repo rates)

2) computing the price of a bond (discounting all cash flows) with a settlement date on T.

And if I were to compute the DV01 of a Treasury future, are both of these acceptable:

a) Compute the change in forward price as defined in 1) when tweaking par yields and repo rates, with the forward date being hte delivery date of the future contract.

b) Compute the change in price of a bond as defined 2), with the settlement being the delivery date of the contract, a conversion factor applied to the result.

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  • $\begingroup$ In method 2 above, can't we first discount all cash flows to the "spot date" (The only difference with the spot dirty price would be if any coupons is paid between spot date and forward date), and then capitalize back to the forward date T using the carry curve (e.g. Repo curve)? $\endgroup$ – benjbe Jan 7 at 9:14
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With regard to your first question: theoretically, these two methods should produce the same forward price. In practice, they might not. This is because a lot of (most?) institutions build the front end of the bond curve using short-term Treasuries. The forward price calculated using such a curve (as discounted present value) effectively assumes the forward position is financed at short-term Treasury rates. By contrast, your "spot - carry" calculation mostly likely uses repo financing. Since repo trades at a spread to Treasury rates, the two answers will differ slightly. If your yield curve is built with repo rates at the front end, you'd have no problems. (There's another reason why the two answers might differ, which boils down to what market convention you use to calculate your carry, see formula for forward price of bond for details.)

As to bond futures DV01, it is most often calculated by shifting the yields of the entire delivery basket by $x$ basis points, holding repo rates constant, and then apply a bond futures model to see how much price changes by (a model is needed to account for changes in delivery option value). You have the options of shifting either the spot yield or the forward yield; you should discuss with your traders to see whether they have any preferences.

You can also hold bond yields constant and shift the repo curve, which produces the "rho" (sensitivity to financing rate).

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Theoretically, both methods should give same result. But practically, term repo market is very illiquid (wide bid-offer that become wider further out you go, though you might find quotes for term repos to bond future delivery dates) plus the discount curve is never fully defined for bond markets, traders use their intuition to build one - unique curve does not exist. These two issues will give differences.

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