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For stochastic volatility models, and any vol model I know, it seems the standard approach is to calibrate the model from option prices. As other user said, this seems a chicken egg problem - how do I price options if I have to calibrate model from option prices?.

Atiya and Wall (2009) show how to obtain the maximum likelihood estimates of the physical parameters of the Heston model using a time series of historical stock prices. “An Analytic Approximation of the Likelihood Function for the Heston Model Volatility Estimation Problem.” But still, this is under physical measure P and not Q risk neutral.

For Heston, Stein&Stein, or any stoch vol, even local vol models...is there any other approach to calibrate parameters from stock prices -and not option prices?-. The question arrises particularly when there is no current option market in a given exchange/country so no actual option data to calibrate any kind of model, just data from the underlying.

Best,

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In an incomplete market, vanilla options are independent assets like stocks or bonds. So the best way of thinking about how they are priced is the same way equilibrium prices in those markets occur: If too many people try to buy an option at a given strike then they push the price of those options up and we see that as the implied volatility increasing. The real thing here is the price of the option increasing, the implied volatility is a quoting convention but secondary to the dollar price. The opposite happens if too many people try sell a given strike in the market.

The models required in equilibrium markets are different to those required in derived markets. In fact you do not need a model if the market is liquid enough. You could be doing technical analysis on charts and thinking implied volatility is historically low and supported by some future event and thus bid and offer accordingly. Once again think stocks, not black-scholes. Pretty much all vanilla markets work this way, from credit and bonds to fx and equities. Remember people were trading options way before the Black-Scholes-Merton papers.

You need a complex model if you want to derive some exotic options value from the base market where your world of hedging instruments include vanilla options and the underlying instruments. The model gives you a arbitrage free way of interpolating the prices of your base instruments and vanilla options and thus arriving at your exotic options value. That is the reason you calibrate this models - they are fancy interpolators and require base information to interpolate from.

Now if you find yourself in a market where vanilla options do not trade, then pick the simplest model you can intuit to map your intuition to option prices and behave accordingly. There is a reason black-scholes is everywhere! If you must price an exotic in that environment then an uncertain volatility model is not a bad first stab as the parameters once again allow you to interpolate from what you know (perhaps some historical upper and lower realized volatility bounds) into option prices.

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  • $\begingroup$ +1 I think Derman called them extrapolators, not interpolators, as in ‘we expand the product universe in a sane way’ 😄 $\endgroup$ – ir7 Sep 17 at 3:22

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