Backtesting Local Volatility for AUD/USD Option Hedging

Summary

This paper tests whether the local volatility model is useful for hedging AUD/USD vanilla options. Local volatility extends Black-Scholes by allowing volatility to depend on time and the underlying exchange rate, and it can be calibrated to fit an implied-volatility surface. The authors emphasize that fitting current market prices is not enough to validate a model: models calibrated to current conditions need to be recalibrated over time, and their hedging performance should be checked against historical outcomes.

The backtests use AUD/USD implied-volatility data from 2005 to 2011 and examine delta-hedging errors across option maturities and strikes. They compare sticky-delta hedging with theoretically correct delta hedging. The reported results find that standard Black-Scholes has hedging errors no worse than local volatility, and performs significantly better for in-the-money and at-the-money options. The excerpt does not give error metrics, costs, or details about market regimes, which limits conclusions about out-of-sample performance or practical trading profitability.

Key ideas

• A current implied-volatility fit does not by itself establish that a pricing model hedges well.
• The study backtests AUD/USD option delta hedges using historical data from 2005 to 2011.
• It compares local volatility and Black-Scholes across strikes and maturities under two delta-hedging approaches.
• Black-Scholes hedging errors are reported as no worse overall and significantly better for in-the-money and at-the-money options.
• The excerpt omits error metrics and transaction costs, limiting assessment of real-world profitability.

Tags

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


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









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.

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