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Hedging efficiently under correlation

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  • Roberto Daluiso
  • Massimo Morini

Abstract

We show that when a derivative portfolio has different correlated underlyings, hedging using classical greeks (first-order derivatives) is not the best possible choice. We first show how to adjust greeks to take correlation into account and reduce P&L volatility. Then we embed correlation-adjusted greeks in a global hedging strategy that reduces cost of hedging without increasing P&L volatility, by optimization of hedge re-adjustments. The strategy is justified in terms of a balance between transaction costs and risk-aversion, but, unlike more complex proposals from previous literature, it is completely defined by observable parameters, geometrically intuitive, and easy to implement for an arbitrary number of risk factors. We test our findings on a CVA hedging example. We first consider daily re-hedging: in this test, correlation-adjusted greeks allow the reduction of P&L volatility by more than 30% compared to standard deltas. Then we apply our general strategy to a context where a CVA portfolio is exposed to both credit and interest rate risk. The strategy keeps P&L volatility in line with daily standard delta-hedging, but with massive cost-saving: only six rebalances of the illiquid credit hedge are performed, over a period of six months.

Suggested Citation

  • Roberto Daluiso & Massimo Morini, 2017. "Hedging efficiently under correlation," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1535-1547, October.
    • Handle: RePEc:taf:quantf:v:17:y:2017:i:10:p:1535-1547
    DOI: 10.1080/14697688.2017.1299201
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    References listed on IDEAS

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    1. Dhaene, Jan & Linders, Daniël & Schoutens, Wim & Vyncke, David, 2012. "The Herd Behavior Index: A new measure for the implied degree of co-movement in stock markets," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 357-370.
    2. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    3. A. E. Whalley & P. Wilmott, 1997. "An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 307-324, July.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    Cited by:

    1. Tak Kuen Siu & Robert J. Elliott, 2019. "Hedging Options In A Doubly Markov-Modulated Financial Market Via Stochastic Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-41, December.
    2. Barletta, Andrea & Santucci de Magistris, Paolo & Sloth, David, 2019. "It only takes a few moments to hedge options," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 251-269.
    3. Pier Francesco Procacci & Tomaso Aste, 2018. "Forecasting market states," Papers 1807.05836, arXiv.org, revised May 2019.
    4. Roberto Daluiso & Marco Pinciroli & Michele Trapletti & Edoardo Vittori, 2023. "CVA Hedging by Risk-Averse Stochastic-Horizon Reinforcement Learning," Papers 2312.14044, arXiv.org.

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