  The Local Volatility model is a well-known extension of the Black-Scholes
constant volatility model whereby the volatility is dependent on both time and
the underlying asset. This model can be calibrated to provide a perfect fit to
a wide range of implied volatility surfaces. The model is easy to calibrate and
still very popular in FX option trading. In this paper we address a question of
validation of the Local Volatility model. Different stochastic models for the
underlying can be calibrated to provide a good fit to the current market data
but should be recalibrated every trading date. A good fit to the current market
data does not imply that the model is appropriate and historical backtesting
should be performed for validation purposes. We study delta hedging errors
under the Local Volatility model using historical data from 2005 to 2011 for
the AUD/USD implied volatility. We performed backtests for a range of option
maturities and strikes using sticky delta and theoretically correct delta
hedging. The results show that delta hedging errors under the standard
Black-Scholes model are no worse than that of the Local Volatility model.
Moreover, for the case of in and at the money options, the hedging error for
the Back-Scholes model is significantly better.
