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I am a bit confused about the practical use of vol surfaces used for derivative pricing. We know that the two main products that best represent market volatility are caps and swaptions, from which volatility surfaces are generated.

I always thought that surfaces implied by the products above described could be used for pricing all products, e.g. barrier options, asian options, CMS and CMS spread options. However, volatility is model dependant, so we could have normal volatility or lognormal volatility.

Therefore, is it the case that we always have to convert a normal/lognormal vol from the corresponding surface to a different volatility, so that it fits the volatility term in our pricing model? For example, what vol do we use if we are using a CIR, HJM or BGM models to price one of the derivatives above described?

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  • $\begingroup$ For these interest rate products, it's actually even worse. I'm unaware of any single model able to accurately price all ir products simultaneously. $\endgroup$ – will Jun 13 '17 at 19:52
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Implied vol surfaces are just a convenient way to represent vanilla options (caps, European swaptions) prices in the context of simple models such as normal, log normal or shifted log normal. When using a more advanced model (BGM, etc.) with the goal of pricing non vanilla options the first step is to calibrate the advanced model vol parameters to vanilla options prices, keeping in mind that non vanilla options may also depend on parameters that can not be captured trough vanilla options (e.g. correlations, or implied vol outside the quoted strikes range, etc.)

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