Valuing the End-of-Month Switch Option in Treasury Bond Basis Analysis

Summary

The document outlines a scenario-based approach to assessing the richness or cheapness of a government bond futures basis and asks how to value the end-of-month switch option. The described steps estimate historical betas for yield changes, apply directional yield shocks, reprice each bond in the delivery basket, and compare carry-adjusted prices after dividing by conversion factors. The bond with the lowest converted price is treated as cheapest to deliver in each scenario.

The unresolved step concerns deriving a hypothetical futures price by assuming the net basis equals the switch option’s value, then calculating net basis for the other bonds. One practitioner reportedly uses the converted price as the futures price, but the question raises concern that this may not resolve the circularity. No valuation formula, worked calculation, or evidence is supplied, so the text frames an implementation problem rather than establishing a solution. Its focus is the delivery option and basis modeling in Treasury bond futures.

Key ideas

• The described basis analysis uses yield-change betas and a matrix of yield shocks to generate bond price scenarios.
• For each scenario, carry-adjusted bond prices are divided by conversion factors to identify the cheapest-to-deliver bond.
• The question centers on how to value the end-of-month switch option when constructing a hypothetical futures price.
• The proposed converted-price shortcut is reported as practitioner practice but is not validated or derived in the document.

Tags

# End of Month Switch Option calculation in Burghardt's Treasury Bond Basis


# End of Month Switch Option calculation in Burghardt's Treasury Bond Basis












Burghardt, in his book, outlines the way one can value the government bond basis and value its richness/cheapness.

The steps are the following:

- Calculate historical betas for yield changes

- Create a bump-matrix where yields are bumped in different directions

- Calculate prices of all bonds in the delivery basket for each bump scenario

- Dividing each bond's price net of carry by the conversion factor.

- For each scenario, the bond with the lowest converted price will be the CTD

- He calculates, for each scenario, a future price 'by assuming that the net basis equals the value of the end-of-month switch option

- 'Armed with this hypothetical future price, the net basis is calculated for all the non-cheap bonds'

My issue is with point 6. How is the 'value of the end-of-month' switch option calculated? He doesn't explain how to do this in the book. One practitioner told me that, because this is a circular problem, they just take the converted price to be the future price - and calculate the net basis from there - however I'm not convinced.

Thank you

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.