Historical Backtesting of Local Volatility Model using AUD/USD Vanilla Options

TL;DR

This paper evaluates the effectiveness of the Local Volatility model for AUD/USD options by performing historical backtests and comparing delta hedging errors to the Black-Scholes model.

Contribution

It provides a comprehensive backtesting analysis of the Local Volatility model's performance in FX options, highlighting its limitations compared to Black-Scholes.

Findings

Delta hedging errors are similar for both models.

Black-Scholes model performs better for at-the-money options.

Historical data from 2005-2011 was used for validation.

Abstract

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.