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回测局部波动率对 AUD/USD 期权的对冲表现

文章 arXiv papers · 作者: Timothy G. Ling et al.
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总结

本文检验局部波动率模型是否适用于对冲 AUD/USD 普通期权。局部波动率模型扩展了 Black-Scholes 模型，允许波动率取决于时间和标的汇率，并可通过校准拟合隐含波动率曲面。作者强调，仅拟合当前市场价格不足以验证模型：根据当前条件校准的模型需要随时间重新校准，并应根据历史结果检查其对冲表现。

回测使用 AUD/USD 的隐含波动率数据，涵盖 2005 至 2011 年，并考察不同期权到期日和行权价下的 delta 对冲误差。研究比较了粘性 delta 对冲与理论上正确的 delta 对冲。报告结果显示，标准 Black-Scholes 的对冲误差不高于局部波动率模型；对于实值和价平期权，其表现显著更好。摘录没有给出误差指标、成本或市场状态细节，因此难以判断样本外表现或实际交易盈利能力。

核心观点

  • 拟合当前隐含波动率并不能单独证明定价模型具有良好的对冲表现。
  • 研究使用 2005 至 2011 年的历史数据，对 AUD/USD 期权 delta 对冲进行回测。
  • 研究在两种 delta 对冲方法下，按行权价和到期日比较局部波动率与 Black-Scholes 模型。
  • 据报告，Black-Scholes 的整体对冲误差不高于局部波动率模型，对实值和价平期权则显著更好。
  • 摘录未提供误差指标和交易成本，因此难以评估实际盈利能力。

标签

外汇期权波动率回测风险管理
全文
# 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.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。