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 ?