Journal of Computational Finance

Risk.net

Local variance gamma revisited

Markus Falck and Mikhail Deryabin

  • We propose a new method for volatility surface construction for FX-options. The result is a sufficiently smooth explicit parameterization of option prices. 
  • Our results suggest that the model produces volatility surfaces that fit market quotes with an error of few volatility basis points and with calibration time less than 1 ms per expiry.
  • We extend the model to allow for interpolation between expiries and present sufficient conditions for absence of arbitrage. 
  • We apply the calibrated modes to construct local volatility surfaces and for pricing variance swaps.  

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.
 

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