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Joined: July 26th, 2010, 12:27 am

Volatility smiles in practice

October 28th, 2014, 11:35 am

I've never been in such a position myself, but I believe that e.g. on the sell side, a volatility smile, or more generally a vol surface, is used to price instruments including vanilla options.If yes, then my question is about fitting a vol smile with calls and puts. If they are both European and the underlying pays no dividends then calls at puts at the same strike (tenor is fixed here) will have the same implied volatility by Put-Call Parity and standard theory. But in practice the theoretical assumptions are only approximations so the implied vols will be a bit off (if I recall I have observed this). Moreover, if there are dividends or the options are American then the theory may not even give the same implied vol.My question is how this is handled in practice? Is a single vol smile used? Do they live they live with the error that both calls and puts at a given strike cannot be priced correctly? Is more than one smile used, or is some adjustment made depending on whether a call or put is being priced?
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Volatility smiles in practice

October 28th, 2014, 1:44 pm

Here is what I would consider normative practice.Strive to create a single smooth, euro-style, arbitrage-free, implied-vol smile out of market quotes. As a first step in that, I would collect quotes from exclusively out-of-the-money options with positive bids. In US listed options, the market I am most familiar with, I have yet to see a case where this cannot be sensibly done.If you can show a problem area, please do so, as I don't claim to have seen everything.Trickiest, but still falling under this umbrella, are 'hard-to-borrow' and non-tradable underlyings, which are common. That fitted smile, if correctly translated back to prices (which may be amer-style), typically runs in-between the bid-ask option quotes for both puts and calls, both in-and-out of the money.When that happens, I would say there is no practical error. I am not claiming that no-practical-error always results.But when it doesn't, the most likely explanations are a poor implied-vol fitting procedure and/or a stale quote.
Last edited by Alan on October 27th, 2014, 11:00 pm, edited 1 time in total.

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