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 ?

  • 2
    $\begingroup$ Unclear what you mean. The calculation of futures convexity adjustments has nothing to do with American vs European. $\endgroup$
    – dm63
    Jul 27, 2023 at 10:42
  • $\begingroup$ Unclear what you mean. I never wrote that futures convexity has anything to do with european vs american. I wrote that to compute the convexity of a given futures I need to calibrate some model on a set of options on that futures and that those options (see CME) are american options, so that the choice of the model witll have to take into account the fact that pricing of american options of this futures will have to be fast as it will be used for calibration. $\endgroup$ Jul 27, 2023 at 19:34
  • $\begingroup$ I editied the question. $\endgroup$ Jul 27, 2023 at 19:35

2 Answers 2


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.


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.

  • $\begingroup$ Both these models will need the SOFR curve in input (among other inputs) and I am bootstrapping/calibrating it. Should I bootstrap an SOFR curve by neglecting convexity first and use that "pre-curve" as input in those models ? Regarding the second model on Bloomberg as far as I remember as saw Ho-Lee and Hull-White and always thought they were 1F models. Fair point for the need of a 2F model, but just for the bootstrap matter would a 1F suffice ? $\endgroup$ Jul 28, 2023 at 14:29
  • $\begingroup$ Yes to the first question ! $\endgroup$
    – dm63
    Jul 28, 2023 at 23:06
  • $\begingroup$ Good, thx. And the second?... :) $\endgroup$ Jul 29, 2023 at 5:38
  • $\begingroup$ 1F will slightly overestimate the convexity I believe. $\endgroup$
    – dm63
    Jul 31, 2023 at 19:38

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