Pricing Interest Rate/Treasury Bond Futures

  • The pricing of Treasury bond futures is performed in the same formulaic manner as presented earlier in the futures section.

  • Note that the spot price includes any accrued interest for the bond.

  • The Treasury bond future price must be divided by the conversion factor.

  • Because the futures contract seller is allowed to deliver from a range of bonds at expiration to fulfill the contract, a conversion factor must be applied to the futures price.

  • Treasury bond pricing is based on the "cheapest to deliver" (CTD) bond as this would be the most rational decision for the futures contract seller.

  • Step 1: Price Treasury Bond Future

Treasury Bond Futures Price: f0(T) = [S0 - PV(CF)](1+r)T

Treasury Bond Futures Price (alternative formula): f0(T) = S0(1+r)T - FV(CF)

  • CF = Coupon payment during the remaining life of the contract term

  • S0 = Full bond price, including accrued interest

  • Step 2: Apply the Conversion Factor

Treasury Bond Price = Futures Price of the CTD/Conversion factor

Note: expect the exam to provide the CTD bond and the conversion factor. The test taker may be required to price a futures contract, given that data.

Either of the formulas from step 1 could be divided by the conversion factor; either would yield the same result.

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