Why does the cheapest-to-deliver bond switch and how should traders model this option?

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AcadiFi · Accepted Answer

The cheapest-to-deliver (CTD) bond is the one that minimizes the short's delivery cost: P_bond - Futures * CF. For yields above the 6% notional coupon, longer-duration, lower-coupon bonds tend to be CTD; below 6%, shorter, higher-coupon bonds dominate. The short holds an embedded switch option valuable because yields might cross the 6% threshold before delivery. Consider Marigold Rates Fund short June futures: currently the 2.5% of 2032 is CTD at 10-year yield 4.8%. If yields drop to 3.5%, the 4.75% of 2034 becomes cheaper. The switch option is priced using yield-curve simulations and rises in value with volatility and time to delivery. Ignoring this option overstates the theoretical futures price; the market-implied futures price is therefore below the static cost-of-carry level. Traders model it via Monte Carlo over the short-rate or by computing CTD across scenarios and taking the minimum.

A reasonable approximation values the switch option at 15-25 bps for a 3-month horizon when yields are near 6%, and near zero when yields are far from the threshold. This option decays sharply into the delivery month.

Why does the cheapest-to-deliver bond switch and how should traders model this option?

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