Implied Volatility in the Variance Gamma Model

This Demonstration explores the implied volatility "smile" and "skews" for the variance gamma model. "Implied volatility" means the value of the volatility parameter in the Black–Scholes model (assumed to be constant in the model), which gives the same option value as the one quoted on an options exchange. It is well known that implied volatility for market option prices when plotted against the strike price shows "skews" and "smiles". This Demonstration shows that skews and smiles are also obtained if, instead of market option prices, you use option prices generated by the three-parameter variance gamma model.