Choosing Inputs for Black–76 Implied Volatility on SPX Options

Summary

The document asks how to select inputs for calculating Black–76 implied volatility on an SPX option. The author describes using a continuously compounded rate interpolated from the US Treasury par yield curve, deriving the forward from that rate and put–call parity, measuring time precisely to expiration without removing weekends, and using the option’s midpoint price.

It gives one dated SPX weekly call example, with its time to expiration, rate, forward level, midpoint, and resulting implied volatility. These figures illustrate the author’s chosen convention; the document does not compare alternative rate curves, forward estimates, or price marks, nor establish that this convention is canonical. The example also leaves practical choices such as dividend treatment, quote quality, and interpolation details open, so the result should be read as a worked input setup rather than a universal prescription.

Key ideas

• Black–76 implied volatility depends on choices for the rate, forward, expiry time, and option price.
• The author derives the forward using the rate and put–call parity.
• The example uses exact calendar time to expiration and the option midpoint.
• A single example illustrates the input convention but does not establish it as canonical.

Tags

# Canonical choice of inputs for Black76 model?


# Canonical choice of inputs for Black76 model?












What is the canonical choice of inputs (e.g. interest rate, forward price, option price, time to expiration, etc) for the Black76 model? For concreteness let's say on the SPX index.

I am using the Daily Treasury Par Yield Curve to interpolate a continuous rate, I use this rate and put-call parity to work out a forward price, I take the exact time to expiration (I don't factor out weekends), and use the mid-price of the option.

For example, for `SPXW240809C05350000` at `UTC: 2024-08-02 20:00:00+00:00` I have `T: 0.0192 r: 0.0549 F:5350.00` and a mid-price of `63.55` and get a vol of `21.52%`.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.