Filling the gaps

Calibrating a local volatility model to options prices is a complicated process requiring both interpolation of liquid prices and extrapolation beyond them. Recently focus has turned to efficient numerical methods. Here, Alex Lipton and Artur Sepp show how to improve this using a classical analytic tool

Some of the most fundamental and long-considered solved problems of financial engineering, such as construction of yield curves and calibration of implied volatility surfaces, have recently turned out to be more complex than previously thought.

In particular, it has become apparent that one of the main challenges of options pricing and risk management is the sparseness of market data for model calibration, especially in severe conditions. Market quotes can be very sparse in both strike and