Abstract
1. Robin Grieves 1. A senior fellow at the Nanyang Technological University, Singapore (robin_grieves{at}yahoo.com) 2. Alan J. Marcus 1. At the Boston College, Wallace E. Carroll School of Management in Chestnut Hill, MA. (alan.marcus{at}bc.edu) A widely used approach for calculating hedge ratios for Treasury futures contracts assumes that the contract will be settled with the currently cheapest–to–deliver note or bond. With that single–deliverable assumption, the futures’ PVBP (price value of a basis point) is the converted, forward PVBP of $100,000 par of the cheapest to deliver. In reality, however, as market yields fluctuate, the identity of the cheapest–to–deliver bond may change. The authors derive the PVBP for futures contracts using an exchange option model and show that the futures’ PVBP accounting for the uncertainty in the ultimate delivery bond is typically very different from the PVBP implied by a single–deliverable model. Explicitly accounting for the fair value of the futures price eliminates the discontinuity and instability that otherwise would characterize the interest rate sensitivity of the futures contract. Finally, the two–deliverable model allows for futures hedge ratios to exhibit negative convexity that is not possible in a single–deliverable model.
Published Version
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