How does the cheapest-to-deliver switch option work in Treasury bond futures, and when does the CTD bond change?

The cheapest-to-deliver (CTD) switch option is a valuable embedded option held by the short in a Treasury bond futures contract. It arises because the conversion factor system, which attempts to normalize different deliverable bonds to a 6% coupon equivalent, is imperfect. As interest rates change, a different bond may become cheapest to deliver, giving the short the option to switch.\n\nConversion Factor Mechanics:\n\nThe invoice price the short receives at delivery is:\n\nInvoice = Futures Price x CF + Accrued Interest\n\nThe delivery cost is the bond's market price plus accrued interest. The short chooses the bond that maximizes:\n\nDelivery Profit = (Futures Price x CF) - Clean Market Price\n\nEquivalently, the CTD minimizes: Clean Price - (Futures Price x CF), known as the basis net of carry.\n\n`mermaid\ngraph TD\n A[\"Yields BELOW 6%\"] --> B[\"CF system overvalues
high-coupon bonds\"]\n B --> C[\"Low-coupon, long-duration
bonds become CTD\"]\n D[\"Yields ABOVE 6%\"] --> E[\"CF system overvalues
low-coupon bonds\"]\n E --> F[\"High-coupon, short-duration
bonds become CTD\"]\n G[\"Yields AT 6%\"] --> H[\"All bonds roughly
equally cheap to deliver\"]\n C --> I[\"Short benefits if
rates fall further\"]\n F --> J[\"Short benefits if
rates rise further\"]\n`\n\nWorked Example:\n\nRidgemont Capital is short 100 T-bond futures contracts ($10M notional). Two deliverable bonds are:\n\n| Bond | Coupon | Maturity | CF | Clean Price |\n|---|---|---|---|---|\n| Bond A | 4.25% | 2046 | 0.7814 | $94.50 |\n| Bond B | 6.75% | 2043 | 1.0567 | $108.25 |\n\nFutures price = $121.00\n\nDelivery profit per bond:\n- Bond A: (121.00 x 0.7814) - 94.50 = 94.5494 - 94.50 = $0.0494\n- Bond B: (121.00 x 1.0567) - 108.25 = 127.8607 - 108.25 = -$0.3893 (loss)\n\nBond A is CTD. If rates drop 100 bps, Bond A's longer duration causes its price to rise more, potentially making Bond B the new CTD. This switch represents the option value.\n\nWhy the CTD Switches:\n\nThe conversion factor is calculated assuming a flat 6% yield curve. When actual yields deviate from 6%, the CF systematically misprices bonds with durations different from the contract's target. Duration dispersion among deliverable bonds directly drives switch option value -- wider dispersion means more optionality.\n\nValue of the Switch Option:\n\nThe switch option compresses the basis (futures trade slightly below theoretical fair value) because the short holds this optionality. In volatile rate environments, the switch option can be worth 5-15 ticks ($156-$469 per contract), which hedgers must account for in basis trading strategies.\n\nPractice CTD identification problems in our FRM question bank.