There is abundant literature discussing the pricing of Bermudan swaptions and the relevance of single-factor Markov-functional models (e.g. LGM) versus multi-factor market models (e.g. LMM).

From a famous paper by Andersen & Andreasen (and other research comparing the empirical hedging performances of various approaches), Bermudan swaption prices seem to depend only weakly on the number of factors of the underlying model. From what I've gathered, the market standard on the sell-side is then to use a LGM calibrated à la Hagan.

This simple framework effectively allows to express the price of a Bermudan swaption as a function of the relevant coterminal swaptions and a mean reversion term structure. The idea is that while the former determine the marginal future swap rates distributions, the latter can be tuned to impose their correlation, which seems to be the true relevant risk-factor here (compared to smile).

A question which I have never seen mentioned though is Can the same model and calibration strategy can be used to quote both payer and receiver Bermudan swaptions.

In an attempt to answer this question, I've calibrated a plain LGM model on coterminals with same strike as my Bermuda and compared output payer vs. receiver prices (expressed as a spread of the relevant most-expensive coterminal as per market standard). My conclusion is that I can never simultaneously fit both.

On one hand, it is not much of a surprise as:

  • The exercise boundary of a payer vs. receiver Bermudan are not the same in the swap rate dimension (one being above, the other below, the strike level). I would therefore suspect smile to have a role to play here. But literature seems to indicate this effect is marginal when compared to the correlation effect, with 'local volatility' models à la Cheyette not adding much.
  • Payer vs. receiver Bermudans do not really depend on the same risk factors at the end of the day. Stretching the comparison to the extreme, it would be like comparing an American call versus put with a steep forward curve. These two options would have very different optimal exercise time hence depend on smiles at two very different maturities. Again is the correlation between swap rates to capture this effect or does should this motivate us to use two distinct 'implied' LGM dynamics for payer vs. receiver. In the latter case, how to prove that it does not lead to arbitrage opportunities?

Anyway, I would be happy if you could share your expert thoughts on this one!


1 Answer 1


I’m guessing you are finding that your model overvalues Bermudan receiver options and probably undervalues Bermudan payer options. The rationale for this has more to do with supply and demand than theory. That’s because every time a callable bond is issued and swapped, dealers buy Bermudan receiver options, so there’s a huge supply. For Bermudan payers there is no such analogy.

Because of this supply and demand situation, Bermudan receivers tend to be overvalued by any reasonable model relative to the market. In order to deal with this, various market practices have evolved. Probably the most popular is to suppress a subset of the options such that the valuation is more in line with the market. For example , suppressing options expiring > N years. Or retaining only the maximal set of 2 coterminals. Such practices are not needed for Bermudan payers options.

  • 1
    $\begingroup$ Thanks for the very useful practical insight. I was wondering if this could be explained by a market asymmetry indeed. I confirm what you suspect: when I calibrate to fit Bermudan payers (for fixed coterminals), I tend to overvalue Bermudan receivers quite strongly, so your explanation makes sense and could be the answer. But if this is the case, does it means that market practice is to quote those as two different instruments (i.e. using two separate dynamics to price & hedge these?) $\endgroup$
    – Quantuple
    Commented May 7, 2021 at 6:06
  • $\begingroup$ Edited the answer $\endgroup$
    – dm63
    Commented May 7, 2021 at 9:42
  • $\begingroup$ This is very helpful already thanks. I suppose there are no references discussing this asymmetry and/or practices? Because while I get that suppressing possible future exercises will mechanically decrease the Bermuda's value, I don't see the link with the trading rationale: why, as a dealer, would I accept to sacrifice a right to exercise in the future since I bought that option for that purpose (hedge) in the first place. Is it because of the cost of capital of holding these options in my books? Or overshooting my limits? $\endgroup$
    – Quantuple
    Commented May 7, 2021 at 21:15
  • 1
    $\begingroup$ This is a long conversation and each dealer has its ‘trade secrets’. Just want to make clear that the dealer is not actually sacrificing any exercise opportunities. Those rights are still in the trade, just not modeled. So they will be a windfall if utilized. $\endgroup$
    – dm63
    Commented May 7, 2021 at 23:07
  • $\begingroup$ Fair enough. Thanks for pointing me on the right direction, I'll wait till the bounty ends just in case it attracts other answers but will accept this one for sure $\endgroup$
    – Quantuple
    Commented May 9, 2021 at 17:12

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