Valuation models
Options on bond and rate futures
Options on bond futures by Black-76 on the price, options on short rate futures by Bachelier or Black on the rate, American exercise by QD+, with Greeks, intrinsic and time value.
Inputs
Results
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Methodology
Conventions
- Options on bond futures: Black-76 on the futures price, discounted from expiry.
- Options on short rate futures (SOFR, Euribor): on the rate 1 − P/100, so a call on the price is a put on the rate.
- American exercise (most listed futures options) uses the QD+ approximation.
References
- Hull, Options, Futures, and Other Derivatives, ch. 18
- CME, Options on SOFR futures
Formulas
- Price
- C = D [F N(d1) − K N(d2)]
- Rate
- f = 1 − F/100, call(F, K) = 100 · put_rate(f, 1 − K/100)