An Expanded Local Variance Gamma model and ultrafast calibration of volatility smile

We propose an expansion of the LVG model that allows for a non-zero drift in the underlying process. A forward ODE is derived that plays a role of Dupire’s equation for the standard local volatility model. Assuming the local... [ view full abstract ]

We propose an expansion of the LVG model that allows for a non-zero drift in the underlying process. A forward ODE is derived that plays a role of Dupire’s equation for the standard local volatility model. Assuming the local variance to be a piecewise linear function of strike and piecewise constant function of time we solve this ODE in closed form. Calibration of the model to the market smiles doesn’t require solving any optimization problem. In contrast, it can be done term-by-term by solving a system of non-linear algebraic equations for each maturity, and thus is ultrafast.