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This might seem like a dumb question.

When using a volatility model, stochastic for example, we try to calibrate it so that it fits the implied volatility smile given by the market, but why is this volatility smile so important ? What can we do with our calibrated smile afterwards ? I read here and there that we can reprice exotic products afterwards or interpolate to get an implied volatility for a strike that is not listed on the market, but can you give more detail ? If possible using SABR or any other model as an example ?

Thank you

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  • $\begingroup$ Yes, knowing the smile allows you to price exotics correctly. smartquant.com/references/OptionPricing/option14.pdf $\endgroup$ – noob2 Aug 23 '17 at 23:54
  • $\begingroup$ This really depends on what type of 'exotic product'. For instance, a forward start option depends on the future smile, so it is not enough to only fit the current state of the vanilla market. Volatility models (be it stochastic or local or whatever) embed such a future smile dynamics and can be useful for that. Still, this may not be enough if you're trying to simultaneously price options on an equity and contracts on the associated realised variance. So it all depends on what you are trying to achieve. $\endgroup$ – Quantuple Aug 24 '17 at 8:09
  • $\begingroup$ I should add that knowledge of the skew (or rather its dynamics) is also important for risk management purposes. If you have a big option portfolio you are "exposed" to changes in skew and so it is in your interest to keep track of it. So skew is important for valuation of SOME exotic options and for risk management of big option portfolios. My two cents. $\endgroup$ – noob2 Aug 25 '17 at 13:04
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Any model that you would like to use for literally anything option-related can be assessed on the grounds of ability to replicate real-world phenomena that we see around, called stylized facts. Volatility smile is one such stylized fact, and a very important one too, as it is so widespread and easy to detect (in stocks, bonds, FX etc.) and thus constitutes the most obvious test for your model. If the model cannot pass it, you should probably consider another.

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It is not important if you want to price only ATM swaptions. However, if you need to price swaptions that are not ATM it becomes important.

E.g. if you are buying selling away-from-the-money swaptions, or if you have "old" swaptions in your portfolio that you need to calculate the fair value of (because you need to call or pay cash colleteral).

It has not so much to do with "exotic" products.

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