基于AUD/USD香草期权的局部波动率模型的历史回测
Historical Backtesting of Local Volatility Model using AUD/USD Vanilla Options
摘要：
局部波动率模型是Black-Scholes常数波动率模型的著名扩展，其中波动率取决于时间和标的资产。这个模型可以被校准，以提供一个完美的拟合范围广泛的隐含波动率表面。该模型易于校准，在外汇期权交易中仍然非常受欢迎。在本文中，我们解决了本地波动率模型的验证问题。可以对标的物的不同随机模型进行校准，以提供与当前市场数据的良好拟合，但应在每个交易日重新校准。与当前市场数据的良好拟合并不意味着该模型是适当的，应进行历史回溯测试以进行验证。本文利用2005 - 2011年澳元/美元隐含波动率的历史数据，在局部波动率模型下研究了德尔塔对冲误差。我们使用粘性Delta和理论上正确的德尔塔对冲对一系列期权到期日和执行价格进行了回测。结果表明，标准布莱克-斯科尔斯模型下的德尔塔对冲误差并不比局部波动率模型下的差。此外，对于在和在货币期权的情况下，对冲误差的Back-Scholes模型是显着更好。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
