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SABR for Equity Options: Drift Assumptions and Practical Use

Article Quant Q&A · Author: Sanjay
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Summary

This note raises a modeling question about applying SABR to equity options. It sketches a stock process in which instantaneous volatility is stochastic and the stock diffusion is scaled by a power of the stock price. The author questions the absence of a drift term, reasoning that this feature makes SABR seem less natural for equities than for foreign exchange.

The document does not include an answer, evidence about bank or dealer practice, calibration results, or a comparison with alternative models. Its useful content is therefore the distinction between a model’s risk-neutral pricing dynamics and the real-world drift intuition that motivates the question. It leaves unresolved whether equity implementations incorporate carry or dividends elsewhere, how the model is adapted in practice, and which option features determine its suitability.

Key ideas

  • The document asks whether financial firms use SABR to price equity options.
  • It describes a stock diffusion whose volatility is stochastic and whose scale depends on the stock level.
  • The author questions the lack of an explicit drift term in that process.
  • No practical industry evidence or resolution to the modeling question is provided.

Tags

EquitiesOptionsVolatilityDerivatives pricing
Full text
# Is SABR being used in practice for Equity options


# Is SABR being used in practice for Equity options












Just to be clear: By "in practice" I mean what the banks and other financial companies do.

Do financial companies use SABR for pricing equity options?

Consider a stock with price $t$ being: $S_t$. In SABR model we define the stock dynamics will be:

$$dS_t=S_t^{\beta}\sigma_tdW_t$$ and a process for the volatility. I believe it is not a very good practice to assume no drift for a stock. So that is why I have difficulty understanding how people can use SBAR in practice for Equity while it does make more sense to us it in FX for instance..

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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