SOFR Futures Convexity Adjustments and Option Model Calibration
Summary
The discussion considers how to account for convexity when bootstrapping a SOFR curve with futures and swaps. It distinguishes the task of calibrating to American options on SOFR futures from estimating futures convexity, and outlines approaches proposed by contributors. One suggestion is to convert American option prices to European equivalents by estimating early exercise value, then use a two-factor model for convexity because the adjustment depends on volatility and correlation. Another recommends an ATM-calibrated Hull–White model for futures convexity; a separate comment suggests using cap or floor volatility inputs for simple one-factor models.
The replies describe practitioner opinions rather than a consensus standard. They indicate that American exercise effects may be small for these options, but the document offers no supporting data or detailed implementation. The initial question raises tree and PDE pricing for calibration, yet the answers do not compare their speed or accuracy. Model choice and volatility inputs therefore require further validation for a particular curve and market setup.
Key ideas
- American option prices may need adjustment to European equivalents before model calibration.
- A one-factor model can be used to estimate the early exercise component.
- The described convexity adjustment depends on both volatility and intracurve correlation, motivating a two-factor model.
- An ATM-calibrated Hull–White model is proposed for SOFR futures convexity.
- The replies present possible practices but do not establish a market-wide standard.
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# SOFR futures options # SOFR futures options I am trying to take convexity adjustments into account in the bootstrap on the SOFR curve. I am using cash for the upfront, SOFR swaps from 2Y to the end. In the mid term I use 2 1M SOFR futures and 7 3M SOFR futures. For each of the 9 futures I want to calibrate a simple model (Ho-Lee or maybe Vasicek) to on a small implied vol surface to price the convexity. What is the market practice ? The implied vol surface quotes I have to calibrate the model on are quotes of american options (and their prices is not theoretically the same as the price of their corresponding european options as because of the collateral an early exercice could be optimal) so that I don't know which model is the best fit regarding this task, as american option should be priced really quick as they will be be used for calibration. Ho-Lee or Hull-White + tree pricer or pde pricer ? ## Answer by df462 (score 0, accepted) https://quant.stackexchange.com/a/76657 Typically for simple 1F models like Ho-Lee or Hull-White, one uses caps/floors flat vol. Back in the day, for Eurodollar futures BBG was defaulting to 10Y cap ATM vol for USD. You can do similar using SOFR caps vol surface. ## Answer by dm63 (score 2) https://quant.stackexchange.com/a/76250 I would recommend 2 steps. First convert your calibration options to European equivalent prices , by estimating the value of the American-ness. This should be small for options on SOFR futures. A simple one factor model should suffice for this. Note that early exercise occurs when the option is deep enough in the money that it is desirable to collect the payoff immediately by exercising into futures. Secondly, in order to estimate the convexity, you will need a 2 factor model because the convexity adjustment depends on the intracurve correlation as well as the volatility. I don’t think there is necessarily a market standard model. ## Answer by Colin Turfus (score 1) https://quant.stackexchange.com/a/83928 I wrote a paper on this called "Analytic Pricing of SOFR Futures Contracts with Smile and Skew" in 2024. Basically I would advise using a Hull-White ATM-calibrated model for the futures convexity. The smile/skew makes no difference until you look at options. I am working on a paper on analytic option pricing: you can price them as Europeans.
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