SABR Calibration Limits and CMS Pricing at Extreme Strikes
Summary
The discussion addresses fitting a single SABR model to swaption, constant maturity swap, and CMS cap markets while managing smile risk. It explains that SABR’s limited number of parameters may not reproduce market prices across a broad strike range, especially at very distant strikes. One practical suggestion is to express strike distance in relative terms, such as delta or percentage of at-the-money, and accept that a good fit over most of the relevant range may be more realistic than a perfect fit everywhere. Manual adjustments and interpolation are mentioned as calibration aids.
For CMS valuation and convexity adjustments, the responses point to alternative research approaches intended to improve consistency or avoid replication formulas that depend on extreme strikes, and recommend a later SABR implied-volatility approximation. These are references rather than worked procedures: the exchange provides no calibration data, comparative tests, or implementation details, so it does not establish which method performs best for a particular portfolio.
Key ideas
- A standard SABR parameterization may lack enough flexibility to fit a complex smile over all strikes.
- Expressing strike distance as delta or relative to at-the-money makes extreme-strike calibration more interpretable.
- A practical calibration may prioritize a good fit across most of the relevant range and use interpolation or manual adjustments.
- CMS convexity and spread-option pricing can require approaches beyond direct fitting of a basic SABR smile.
- The discussion cites methods but provides no empirical comparison or step-by-step implementation.
Tags
Full text
# Sabr practical calibration # Sabr practical calibration What practical methods can be employed to address the calibration challenges of the initial SABR model for very far strikes, particularly in the context of pricing CMS, without over-parameterizing the model, especially when managing a portfolio of interest rate swaptions, CMS, and CMS caps with the goal of hedging smile risk (and also keep getting consistent prices with observed market values) using a single SABR model. ## Answer by THATS MY QUANT MY QUANTITATIVE (score 3) https://quant.stackexchange.com/a/79319 It’s better to quote your strikes as delta’s or %’s because people who aren’t familiar with CMS will have no idea how far away 500 is relatively from ATM. SABR parameterisation struggles to calibrate on many options because of the very few parameters it has. What you’re trying to do is akin to calibrating a quadratic through a cubic-like shape - you don’t have enough parameters to adjust to get a good fit. Calibrating to market sometimes requires a bit of manual adjustments, linear interpolation, guessing etc. If you can get a good fit around 85% of the strike range, that’s already pretty good. ## Answer by Micio Geremia (score 0) https://quant.stackexchange.com/a/83971 To price consistently Swaptions, CMS and CMS options using extreme strikes check Fabio Mercurio and Andrea Pallavicini, "Smiling at Convexity", Risk, August 2006, also available at SSRN: https://ssrn.com/abstract=892287. Regarding the CMS convexity adjustment, check Hagan and Woodward, "An end to replication", Risk, May 2021, also avaible at https://www.researchgate.net/profile/Patrick-Hagan-4/publication/342065574_AN_END_TO_REPLICATION/links/5ee942b192851ce9e7ea3019/AN-END-TO-REPLICATION.pdf which avoids the extreme strikes required by the replication formula. Regarding CMS Spread Options check Hagan, Lesniewski, Skoufis and Woodward, "CMS spread options" https://doi.org/10.1080/14697688.2021.1912379 Remind to use the latest SABR implied volatility approximate formula given in Hagan, Kumar, Lesniewski, Woodward, "Universal Smiles", Wilmott, Volume 2016, Issue 84, July 2016, Pages 40-55, https://doi.org/10.1002/wilm.10523 Please let me know your feedback about these papers.
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