Convexity and Timing Adjustments for SOFR-Based Derivatives

Summary

The document discusses an options-text exercise comparing two quarterly interest-rate payoffs: a spread involving a five-year swap rate and compounded SOFR, and a spread between compounded SOFR and a Treasury bill rate. It reports that the solution manual calls for a convexity adjustment to the swap-rate component in the first case, while deeming timing adjustments unnecessary in both cases.

The questioner challenges the timing conclusion because compounded SOFR is backward-looking, whereas the Treasury bill rate is forward-looking. The excerpt does not include an answer resolving this concern. It highlights the need to distinguish rate observation, accrual, and payment dates, as well as the specific rate conventions and payoff structure when assessing convexity or timing adjustments. The stated solution is reported from the manual, not independently demonstrated here, so the document alone cannot establish whether its reasoning is complete.

Key ideas

• The exercise compares a swap-rate versus compounded-SOFR spread with a compounded-SOFR versus Treasury-bill spread.
• The reported solution calls for a convexity adjustment only for the swap-rate component in the first payoff.
• The question challenges why no timing adjustment is applied to backward-looking compounded SOFR.
• The excerpt provides no resolution, so adjustment requirements cannot be derived from it alone.

Tags

# Exercise 30.2 on Hull's OFOD


# Exercise 30.2 on Hull's OFOD












In Hull's Options, Futures, and Other Derivatives, there is the following exercise in Chapter 30:

> Explain whether any convexity or timing adjustments are necessary when: (a) We wish to value a spread option that pays off every quarter the excess (if any) of the 5-year swap rate over the 3-months compounded SOFR applied to a principal of $100. The payoff occurs 90 days after the rates are observed. (b) We wish to value a derivative that pays off every quarter of the 3-months compounded SOFR minus the 3-months Treasury bill rate. The payoff occurs 90 days after the rates are observed.

The solution manual from the author states that convexity adjustment is necessary for only the swap rate in (a), and the timing adjustment is unnecessary for either.

However, I am having trouble understanding why the timing adjustment is not necessary. I thought that since SOFR is backward-looking, timing adjustment is necessary for compounded SOFR, whereas it is unnecessary for the 3-month T-bill rate since it is forward-looking.

Quite the opposite occurs for the LIBOR

Is there any other point I did not figure out? Or is the solution manual misleading?

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