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Market Volatility and Feedback Effects from Dynamic Hedging

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  • Rüdiger Frey
  • Alexander Stremme
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    Abstract

    In this paper we analyze the manner in which the demand generated by dynamic hedging strategies affects the equilibrium price of the underlying asset. We derive an explicit expression for the transformation of market volatility under the impact of such strategies. It turns out that volatility increases and becomes time and price dependent. The strength of these effects however depends not only on the share of total demand that is due to hedging, but also significantly on the heterogeneity of the distribution of hedged payoffs. We finally discuss in what sense hedging strategies derived from the assumption of constant volatility may still be appropriate even though their implementation obviously violates this assumption. Copyright Blackwell Publishers Inc 1997.

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 7 (1997)
    Issue (Month): 4 ()
    Pages: 351-374

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    Handle: RePEc:bla:mathfi:v:7:y:1997:i:4:p:351-374

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    Cited by:
    1. Jinqiang Yang & Zhaojun Yang, 2012. "Arbitrage-free interval and dynamic hedging in an illiquid market," Quantitative Finance, Taylor & Francis Journals, vol. 13(7), pages 1029-1039, May.
    2. E. Agliardi & R. Andergassen, 2002. "Feedback effects of dynamic hedging strategies in the presence of transaction costs," Working Papers 445, Dipartimento Scienze Economiche, Universita' di Bologna.
    3. Chung, San-Lin & Liu, Wen-Rang & Tsai, Wei-Che, 2014. "The impact of derivatives hedging on the stock market: Evidence from Taiwan’s covered warrants market," Journal of Banking & Finance, Elsevier, vol. 42(C), pages 123-133.
    4. Gill, Ryan & Lee, Kiseop & Song, Seongjoo, 2007. "Computation of estimates in segmented regression and a liquidity effect model," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6459-6475, August.
    5. Ku, Hyejin & Lee, Kiseop & Zhu, Huaiping, 2012. "Discrete time hedging with liquidity risk," Finance Research Letters, Elsevier, vol. 9(3), pages 135-143.
    6. Jon Danielsson & Hyun Song Shin & Jean-Pierre Zigrand, 2012. "Endogenous Extreme Events and the Dual Role of Prices," Annual Review of Economics, Annual Reviews, vol. 4(1), pages 111-129, 07.
    7. Umut Çetin & L. C. G. Rogers, 2007. "Modeling Liquidity Effects In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 15-29.
    8. Daniel Sevcovic, 2007. "An iterative algorithm for evaluating approximations to the optimal exercise boundary for a nonlinear Black-Scholes equation," Papers 0710.5301, arXiv.org.
    9. Emilio Barucci & Paul Malliavin & Maria Elvira Mancino & Roberto Ren� & Anton Thalmaier, 2003. "The Price-Volatility Feedback Rate: An Implementable Mathematical Indicator of Market Stability," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 17-35.
    10. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
    11. Elettra Agliardi & Rainer Andergassen, 2011. "(S,s)-adjustment Strategies and Hedging under Markovian Dynamics," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 36(2), pages 112-131, December.
    12. Joel M. Vanden, 2006. "Portfolio Insurance And Volatility Regime Switching," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 387-417.
    13. Suhas Nayak & George Papanicolaou, 2008. "Market Influence of Portfolio Optimizers," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(1), pages 21-40.
    14. Bronka Rzepkowski, 2003. "Order Flows, Delta Hedging and Exchange Rate Dynamics," Working Papers 2003-18, CEPII research center.
    15. Christian Bauer & Bernhard Herz, 2006. "Monetary and Exchange Rate Stability at the EU. Mediterranean Borders," Revue économique, Presses de Sciences-Po, vol. 57(4), pages 899-917.
    16. R. Andergassen, 2002. "financial contagion and asset price dynamics," Working Papers 448, Dipartimento Scienze Economiche, Universita' di Bologna.
    17. Peter Bank & Dietmar Baum, 2004. "Hedging and Portfolio Optimization in Financial Markets with a Large Trader," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 1-18.
    18. Jarrow, Robert & Protter, Philip, 2005. "Large traders, hidden arbitrage, and complete markets," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2803-2820, November.
    19. M. E. Mancino & S. Ogawa & S. Sanfelici, 2004. "A numerical study of the smile effect in implied volatilities induced by a nonlinear feedback model," Economics Department Working Papers 2004-ME01, Department of Economics, Parma University (Italy).
    20. James Primbs & Muruhan Rathinam, 2009. "Trader Behavior and its Effect on Asset Price Dynamics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(2), pages 151-181.
    21. Thorsten Hens & Stefan Reimann & Bodo Vogt, . "Competitive Nash Equilibria and Two Period Fund Separation," IEW - Working Papers 172, Institute for Empirical Research in Economics - University of Zurich.
    22. Hens, Thorsten & Reimann, Stefan & Vogt, Bodo, 2004. "Nash competitive equilibria and two-period fund separation," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 321-346, June.
    23. Bauer, Christian & Herz, Bernhard, 2009. "Monetary and exchange rate stability in South and East Asia," Pacific-Basin Finance Journal, Elsevier, vol. 17(3), pages 352-371, June.
    24. Astic, Fabian & Touzi, Nizar, 2007. "No arbitrage conditions and liquidity," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 692-708, August.

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