Optimal hedging under fast-varying stochastic volatility
Josselin Garnier and
Papers from arXiv.org
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.
Date: 2018-10, Revised 2020-03
New Economics Papers: this item is included in nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
http://arxiv.org/pdf/1810.08337 Latest version (application/pdf)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1810.08337
Access Statistics for this paper
More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().