SIAM Journal on Financial Mathematics, Volume 11, Issue 1, Page 274-325, January 2020.
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.

中文翻译：

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随机波动下的最优套期保值

SIAM金融数学杂志，第11卷，第1期，第274-325页，2020年1月。
在具有均值或粗糙的均值回复随机波动率的市场中，没有完美的对冲。此处显示了在使用欧式期权的情况下，在此类市场中各种三角型套期保值策略如何执行和评估。对冲成本的精确表征，是由波动率波动引起的复制成本，在波动率波动的快速均值回归的渐近状态下给出。在所考虑的制度中，基于最优动态资产的对冲策略被确定为所谓的从业者三角洲对冲方案。此外，还表明，增量型套期保值方案的绩效基本上与所考虑的制度中波动路径的规律性无关，套期保值成本与维加风险mar相关，其幅度与新的市场风险参数成比例。通过数值模拟还表明，从快速平均均值回复制中的期权价格近似得出的对冲方案是稳健的：当平均均值回复时间为时，从我们的渐近分析中可以看出，从业者的三角洲对冲方案是最优的。在任意平均回复时间下，小似乎是最佳选择。