Pricing Options on Daily-Settled SOFR Futures

Summary

The document asks how to price options on one-month and three-month SOFR futures when the futures themselves are settled daily. It reasons that daily settlement makes a futures price a martingale under the risk-neutral measure because gains and losses are settled and reinvested, then asks whether that reasoning also makes the option price a martingale. It contrasts this setup with options settled at exercise or expiry, for which the writer suggests a forward-measure formulation and Black’s formula may be applicable.

The central issue is how settlement conventions affect the pricing measure and whether daily-settled options require numerical methods. The document provides no answer, derivation, or market data, so it does not establish that the proposed martingale argument is correct or that numerical methods are the only approach. It is a conceptual question about risk-neutral and forward measures, not a pricing recipe.

Key ideas

• The document distinguishes daily settlement of a futures contract from settlement of an option on that future.
• It asks whether daily settlement makes the option price a martingale under the risk-neutral measure.
• It raises the forward measure and Black’s formula as possible tools for options without daily settlement.
• It does not resolve the pricing question or compare analytical and numerical methods.

Tags

# Pricing SOFR Future option


# Pricing SOFR Future option












it might seems maybe trivial but I do struggle in understanding what comes down when pricing options on SOFR 1M and 3M Futures. I understand that under the risk neutral measure, the future price is a martingale since cash flows are continuously settled (daily) which cancels the discounting over time (since we reinvest the cash flow in the cash account). However how does it work for options with the future as underlying? Can we make the assumption that just like futures, daily settled options price are martingale under the risk neutral measure ? Since the discounting over the cumulative PnL is canceling?

If the options was not settled daily, American style or European style, it would be possible to price them using the forward measure (and therefore the Black Formula) to simplify the expectation. In the case of daily settlements, Are numerical methods the only solution to price an exchange traded SOFR Future options?

Is there a misconception in my understanding of derivative pricing under the risk neutral measure and the forward measure?

I would appreciate any help/advice on the subject.

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