SABR Model Limits for Equity and FX Options
Summary
The document asks whether extensions to the SABR stochastic-volatility model, often motivated by rates that can become negative, offer benefits for options on non-negative underlyings such as equities and foreign exchange. The response argues against using SABR or its extensions for those markets, citing the model’s volatility dynamics and resulting implied distributions as poorly aligned with observed behavior, particularly over longer horizons.
It describes SABR’s practical appeal in interest-rate derivatives: a relatively small parameter set, an approximate formula for European options, and computational tractability. Those features can help calibrate a market model across many related instruments, including caps, swaps, and CMS spread products. The response points to a linked paper as context, but presents no comparative tests or quantitative evidence. Its guidance is therefore a stated modeling perspective, not a universal rule; suitability depends on the instrument, horizon, calibration targets, and empirical behavior being modeled.
Key ideas
- SABR extensions can accommodate rate settings that allow negative values.
- The response cautions that SABR volatility dynamics may produce implied distributions inconsistent with empirical equity and FX behavior, especially at longer horizons.
- SABR is described as tractable for interest-rate derivatives because it uses few parameters and has an approximate European-option formula.
- Its simplicity can support calibration of a consistent rates market model across multiple products.
- The document offers an opinion without presenting comparative empirical tests.
Tags
Full text
# Are extended SABR models useful for options with non-negative underlying # Are extended SABR models useful for options with non-negative underlying https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2731359 http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf In the two articles listed above we see several ways to extend the original SABR (Hagan 2002) model and apply numerical schemes to solve it. Both articles mentions low/negative rates as the reason for why these models are useful. How I interpret use of these methods: When the underlying product can be negative then it a good idea too apply these models rather than the original SABR. My question: Is there any advantage in using these extended and more complicated models for options where the price of the underlying cannot be negative? For instance FX and equity options. ## Answer by Phun (score 3, accepted) https://quant.stackexchange.com/a/44539 You don't want to use the SABR (or an extension) to price equity options or FX options. The lag of mean-reversion in the model's volatility dynamics leads to explosive behavior and to a implied distribution that is absolutely not in line with empirics -- especially on longer time horizons. To my knowledge people use it mostly for interest rate derivatives. This is stated by in the linked paper of Jesper Andreasen and Brian Huge as well. The SABR is quite simple since it only relies on 4 Paremeters and it has a quasi-closed form (approximation) formula for European options. So it is numerical quite tractable. One can extend the SABR to a full market model to price different kind of products, like caps, swaps and CMS spreads in one consistent setting. (often more than 50 contracts in total) Here the simplicity of the SABR really counts, because it leads to market models that can relatively easy and fast calibrated.
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