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I'm wondering how we can price a european swaption with a floor on the floating leg. Assuming that we use the HW 1 factor model, how we can simultaneously calibrate the swaption ( on swap rate volatility) and the floor (on the libor volatility).

Do you have any idea how to do this?

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You can't. In a 1 factor model, if you calibrate the libor floor to market, then the swaption prices in the model are likely to be too high versus the market. That's because the difference between swaption prices and cap/floor prices is determined chiefly by the expected decorrelation between different parts of the swap curve , which is not present in the model. You need a richer model such as a multifactor and/or term structure model in order to achieve this.

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  • $\begingroup$ i am sure that there is a technique that let us calibrate both. I have heard by " mapping". It's a thechnique that consiste on prcing the same swaption but with a different stike floor K' such as K' = f(K) ( with K is the old strike floor). but i'm not sure how it works. $\endgroup$
    – Zakariya Alaoui Ismaili
    Commented Dec 24, 2016 at 22:19
  • $\begingroup$ You could price using correct swaption vols , estimate how far off market the floor vol is, then adjust the price by that error * the vega of the floor. The vega of the floor is the difference between the vega of the whole structure and the vega of a similar unfloored structure. $\endgroup$
    – dm63
    Commented Dec 25, 2016 at 13:59

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