英文标题：
《Optimal hedging under fast-varying stochastic volatility》
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作者：
Josselin Garnier, Knut Solna
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最新提交年份：
2020
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英文摘要：
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.
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中文摘要：
在一个具有粗糙或马尔可夫均值回复随机波动性的市场中，没有完美的对冲。这里展示了在欧洲期权的情况下，各种delta型套期保值策略是如何在此类市场中执行和评估的。在波动率波动的快速均值回归渐近机制中，给出了套期保值成本（波动率波动引起的复制成本）的精确表征。在所考虑的制度中，基于资产的最佳动态套期保值策略被确定为所谓的“从业者”三角洲套期保值方案。此外，还表明，delta型套期保值方案的性能基本上独立于所考虑制度中波动路径的规律性，并且套期保值成本与vega风险鞅有关，其大小与新的市场风险参数成正比。数值模拟还表明，从快速均值回归制度下的期权价格近似中得出的拟议套期保值方案是稳健的：当均值回归时间很小时，通过我们的渐近分析确定为最优的“实践者”增量套期保值方案在任意均值回归时间下似乎是最优的。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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