# calibration - negative call price [closed]

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.

• How are you processing the raw prices first? None of your quotes should be negative. – will Dec 13 '19 at 7:28
• I use Lewis pricing formula, and price it with the charecteristic function – LocalMartingale Dec 13 '19 at 11:49

## 2 Answers

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.

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.