The noisy call prices we used were as follows
|Noisy call price as function of the strike price|
|Noise dominates signal|
Our eyes (and the brains behind) see clearly, what the "true" call price curve should be.
Does Pre-Smoothing Help?
A naive approach would be to take averages of noisy data, specifically we take the averages of the point itsellf and its 4 left neighbours and its 4 right neighbours. The averagred prices are drawn in the following plot
|Averaging leads to smaller variance levels|
|Implied volatilities from pre-smoothed noisy data|
These are already much better results. They could be further improved by applying, say, a Gaussian filter instead of naive averaging and by choosing the filter bandwith depending on the level of vega.