The bilateral Gamma motion: Calibration and option pricing

This work considers the calibration of exponential Lévy models to market options data and the subsequent pricing of exotic options. We focus on a natural and promising extension of the bilateral Gamma process that includes a diffusive component. This extension is shown to address a major deficiency in terms of fit quality and shape of the calibrated model volatility surface. The new model, which we call a bilateral Gamma motion, performs well in market calibrations, as demonstrated in several equity market examples, and significantly outperforms the pure-jump bilateral Gamma process. The new model's performance is shown to rival some of the more common alternatives, such as CGMY and jump diffusion models, with consistently strong calibration results. Calibrated model parameters and corresponding exotic option prices are presented, including Asian options, occupation time derivatives (step and fader options), and barrier options. The experiments highlight the sensitivity of various contracts to model assumptions and the importance of model selection and calibration in pricing exotic options.