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I'm a new in financial engeneering and trying to understand basic principles of volatility modelling. I wrote many papers and articles about different models (garch, local vol, stoch vol and ect.) and concluded that one of the main parts of that is calibration model parameters to market prices. It's understood and OK.

But I'm concerned about basic thing. Let's suggest that we haven't options market at all or have very illiquid market (1-2 OTM strikes). How can we quote let's say ATM strikes for some maturities? What are the ways of measure implied volatility in that case?

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If there is no market, there can't be any implied volatility since the latter is derived from the market price :)

In your example, you can just extract implied volatility from the OTM option prices. Then, by choosing some pricing model you can get a price for your ATM option, from which you can get the implied volatility by inverting the Black-Scholes formula.

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  • $\begingroup$ Thanks for the answer. But let's assume that we have some option positions in our portfolio. At some time market begin to move sharply and we have a situation in that no one participant can show market for our options. How can we mark-to-market our portfolio in such circumstances? I suppose that we must have "model" for that cases... $\endgroup$ – spr Nov 27 '19 at 19:05
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    $\begingroup$ @spr Yes in that case having a model would be good. In theory, from a handful of options you should already be able to calibrate a stochastic vol model as these only have a finite number of parameters. It is only for local volatility (or local stochastic volatility) that you need a continuum of options. $\endgroup$ – ilovevolatility Nov 27 '19 at 23:30

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