Bermudan Swaption Pricing with Shifted LMM: Calibration and Model Risks
Summary
The document discusses a callable range accrual note linked to the EUR 20-year versus 10-year CMS spread, with Bermudan exercise. The proposed approach calibrates LIBOR correlations to short-maturity CMS spread options and volatilities to vanilla options. The question is why a shifted LIBOR market model might produce a price above the market level.
The responses emphasize that the non-callable instrument must be valued accurately first. A callable range accrual behaves like a collection of digital payoffs with timing effects, making smile calibration important; discounting and forwarding curves must also be treated separately, and covariance between CMS rates must be captured. A separate market observation attributes model prices above traded levels to abundant supply of Bermudan structures. This is a short discussion rather than a full diagnosis: it provides no calibration results or detailed remedy, and the supply explanation is an experience-based claim rather than demonstrated evidence.
Key ideas
- A callable range accrual’s value depends on modeling its digital-like payoffs and exercise timing.
- Accurate smile calibration is needed to price the corresponding non-callable structure.
- Separate forwarding and discounting curves and CMS rate covariance can materially affect valuation.
- The cited market explanation for lower traded prices is supply of Bermudan structures, but no evidence is presented.
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Full text
# Overpricing Bermudan swaption using Shifted LMM # Overpricing Bermudan swaption using Shifted LMM I am trying to model a callable range accrual note linked to the EUR CMS spread, 20Y-10Y, with cap and floor. The note is Bermudan, callable starting year 3, every 3 years till maturity at 30 year. We plan on using shifted LMM for the EUR rate. We plan to calibrate libor correlations to cms 20-10 spreadoptions 1Y maturity because those are the liquid ones, and vols to vanillas. A colleague told me that we will still overprice the trade. I don't understand why. I understand that Bermudans in will trade at a discount to europeans but I don't understand why the modeling will generally overprice it. Any help or links to papers or books will be greatly appreciated. Also any links to books and papers that explain how to remedy the issue will also be great. Thanks! ## Answer by Mark Joshi (score 2) https://quant.stackexchange.com/a/25706 well there are lots of things to get right... first you need to the non-callable version right, to get that right requires getting the smile right since a callable range accrual is really just a bunch of digitals with timing effects. these days discounting and forwarding are done with different curves so you'll need to get that right too. then you'll need to get covariance between the cms rates right. my paper has some http://ssrn.com/abstract=1461285 ## Answer by dm63 (score 1) https://quant.stackexchange.com/a/25749 When you say 'overprice' I assume you mean model price > market price. In my experience this is true for all reasonable models. It's due to excessive supply of the Bermudan structure in the market.
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