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Im trying to calibrate a stochastic volatility model to market. I end with an MSE of 2-3 with approximately 500 quotes. Some out of the money options with call-price under 1 dollar ends up being negative. I dont know how to plot the implied volatility surface of the model if some of the prices is negative. Any help is appreciated.

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    $\begingroup$ How are you processing the raw prices first? None of your quotes should be negative. $\endgroup$ – will Dec 13 '19 at 7:28
  • $\begingroup$ I use Lewis pricing formula, and price it with the charecteristic function $\endgroup$ – LocalMartingale Dec 13 '19 at 11:49
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It's obviously no calibration problem. It's just a numerical issue. The error resulting from solving the integral numerically is just to big for your really small option price.

I would suggest to cut the wings of your volatility surface at an appropriate moneyness.

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There must me something going wrong since the price of a call is non-negative. This is easy to see from the payoff function, $C$ on an asset, $S$, and strike price $K$.

$$C(S) = \max(0, S - K) \geq 0$$

From the formula we can see that a call at expiry would payout non-negative values, so the price could never fall bellow zero.

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