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快速均值回归波动率下的欧式期权 Delta 对冲

文章 arXiv papers · 作者: Josselin Garnier et al.
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总结

本文比较波动率随机且均值回归时欧式期权的 Delta 对冲策略。在这种情况下，波动率变化使完美复制无法实现，因此分析重点是对冲这些波动所需的额外成本。

研究在波动率快速均值回归的渐近条件下刻画对冲成本，并指出在该条件下，实务人士的 Delta 是最优的动态资产对冲策略。研究将成本与 Vega 风险鞅和市场风险参数联系起来。数值模拟显示，即使均值回归速度不快，该策略可能仍然稳健且表现最佳。这些结论仅适用于所研究的模型和条件；摘录没有提供市场校准或样本外交易证据。

核心观点

  • 在所讨论的情形下，随机波动率使欧式期权无法实现完美对冲。
  • 分析评估波动率快速均值回归时的 Delta 类策略。
  • 研究指出，在快速均值回归条件下，实务人士的 Delta 是最优动态资产对冲方式。
  • 对冲成本与 Vega 风险及市场风险参数相关。
  • 模拟显示，首选策略可能在渐近条件之外仍然有效。

标签

期权波动率衍生品定价风险管理
全文
# Optimal hedging under fast-varying stochastic volatility


# Optimal hedging under fast-varying stochastic volatility









In a market with a rough or Markovian mean-reverting stochastic volatility there is no perfect hedge. Here it is shown how various delta-type hedging strategies perform and can be evaluated in such markets in the case of European options. A precise characterization of the hedging cost, the replication cost caused by the volatility fluctuations, is presented in an asymptotic regime of rapid mean reversion for the volatility fluctuations. The optimal dynamic asset based hedging strategy in the considered regime is identified as the so-called `practitioners' delta hedging scheme. It is moreover shown that the performances of the delta-type hedging schemes are essentially independent of the regularity of the volatility paths in the considered regime and that the hedging costs are related to a vega risk martingale whose magnitude is proportional to a new market risk parameter. It is also shown via numerical simulations that the proposed hedging schemes which derive from option price approximations in the regime of rapid mean reversion, are robust: the `practitioners' delta hedging scheme that is identified as being optimal by our asymptotic analysis when the mean reversion time is small seems to be optimal with arbitrary mean reversion times.

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。