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Applying Shifted SABR to Negative Strikes in Inflation Options

Article Quant Q&A · Author: KP6
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Summary

The document discusses using SABR to price EUR inflation caplets when strikes can be negative, a setting where standard Black and unshifted SABR formulations are not directly applicable. One response recommends reconsidering the model: inflation option prices may be too sparse to support fitting all SABR parameters, and a simpler normalized model calibrated to historical normalized volatility could accommodate negative rates.

Another response suggests applying shifted SABR by shifting both the forward and strike inputs, following the same input adjustment used with shifted lognormal pricing. The exchange offers conceptual guidance rather than a full implementation or calibration procedure, and it does not resolve how to choose the shift or validate the model. Its advice therefore highlights both a practical modeling adjustment and the risk that a parameter-rich model is not identifiable from limited market data.

Key ideas

  • Negative strikes make standard Black and unshifted SABR pricing unsuitable for the stated application.
  • A shifted model applies the shift to both forward and strike inputs.
  • Sparse inflation option prices may not support fitting all SABR parameters reliably.
  • A simpler normalized model calibrated to historical normalized volatility is offered as an alternative.

Tags

OptionsDerivatives pricingVolatility
Full text
# Shifted SABR for negative strikes


# Shifted SABR for negative strikes












I am trying to apply SABR on EUR inflation caplets, with positive forward and negative strikes. Classical BS pricing is undefined, and so is SABR. I have read about the shifted SABR, which is supposed to accept negative strikes, but I was wondering whether anyone is aware of an existing implementation on Matlab for instance.

I have fitted the standard SABR parameters on positive strikes and modified some existing SABR code, adding the shift to the strike and the forward rate in the volatility equation. Now, I am feeding this modified volatility equation with my negative strikes and forward + the fitted SABR parameters, but nothing seems to have changed: it is still impossible to compute vols for negative strikes.

Do I have to feed the original strikes to the shifted model or the shifted strikes ? Do I have to shift the forward as well ? Is anyone aware of a better procedure for using the shifted SABR with negative rates?

Thanks a lot !

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/41135

I would say that SABR is overkill for inflation options, because due to the scarcity of prices for inflation options, there isn't enough information to fit all the SABR parameters. It is probably better to adopt a simple Normalized model of inflation rates, which you can calibrate by looking at historical normalized volatility. This will also take care of your negative rates problem.

## Answer by Micio Geremia (score 0)

https://quant.stackexchange.com/a/83901

Suggestion: go to the simple shifted-lognormal model, then check that you just need to input into your standard black formula (not shifted) the shifted forward, the shifted strike, and anything else a usual. The same happen for shifted lognormal greeks. Just shift the inputs, no additional coding is needed. Then, return to the shifted SABR and use the same logic.

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.