Local Variance Gamma Revisited

Abstract

In this paper, we propose a new method of constructing volatility surfaces for foreign exchange options. This methodology is based on the local variance gamma model developed by P. Carr in 2008. Our model generates smooth volatility surfaces, fits market quotes with an error of a few volatility basis points and allows very fast calibration. Using the Levenberg–Marquardt algorithm, we measure the average calibration time to less than one millisecond per expiry. We suggest a simple and fast yet market-consistent technique for arbitrage-free interpolation of volatility in the maturity dimension, and we derive sufficient conditions for the absence of calendar spread arbitrage within our model. We also apply the methodology to pricing variance swaps.

Keywords: Foreign Exchange (FX) Options, Local Volatility Calibration, Local Variance Gamma, Volatility Interpolation, Variance Swaps