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.
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.