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Liquidity risk, price impacts and the replication problem

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  • Alexandre Roch

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  • Alexandre Roch, 2011. "Liquidity risk, price impacts and the replication problem," Finance and Stochastics, Springer, vol. 15(3), pages 399-419, September.
    • Handle: RePEc:spr:finsto:v:15:y:2011:i:3:p:399-419
    DOI: 10.1007/s00780-011-0156-x
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    References listed on IDEAS

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    1. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    2. 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, January.
    3. Vathana Ly Vath & Mohamed Mnif & Huyên Pham, 2007. "A model of optimal portfolio selection under liquidity risk and price impact," Finance and Stochastics, Springer, vol. 11(1), pages 51-90, January.
    4. Umut Çetin & H. Soner & Nizar Touzi, 2010. "Option hedging for small investors under liquidity costs," Finance and Stochastics, Springer, vol. 14(3), pages 317-341, September.
    5. P. Weber & B. Rosenow, 2005. "Order book approach to price impact," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 357-364.
    6. J. Doyne Farmer & Laszlo Gillemot & Fabrizio Lillo & Szabolcs Mike & Anindya Sen, 2004. "What really causes large price changes?," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 383-397.
    7. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    8. Soner, H. Mete & Cetin, Umut & Touzi, Nizar, 2010. "Option hedging for small investors under liquidity costs," LSE Research Online Documents on Economics 28992, London School of Economics and Political Science, LSE Library.
    9. Philipp Weber & Bernd Rosenow, 2006. "Large stock price changes: volume or liquidity?," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 7-14.
    10. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
    11. Jérôme Detemple & Carlton Osakwe, 2000. "The Valuation of Volatility Options," Review of Finance, European Finance Association, vol. 4(1), pages 21-50.
    12. Umut Çetin & L. C. G. Rogers, 2007. "Modeling Liquidity Effects In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 15-29, January.
    13. 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.
    14. Marcel Blais & Philip Protter, 2010. "An Analysis Of The Supply Curve For Liquidity Risk Through Book Data," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 821-838.
    15. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183, World Scientific Publishing Co. Pte. Ltd..
    16. Robert A. Jarrow, 2008. "Derivative Security Markets, Market Manipulation, and Option Pricing Theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 7, pages 131-151, World Scientific Publishing Co. Pte. Ltd..
    17. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    18. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Panagiotis Christodoulou & Nils Detering & Thilo Meyer-Brandis, 2018. "Local Risk-Minimization With Multiple Assets Under Illiquidity With Applications In Energy Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-44, June.
    2. Masaaki Fujii, 2015. "Optimal Position Management for a Market Maker with Stochastic Price Impacts," CIRJE F-Series CIRJE-F-963, CIRJE, Faculty of Economics, University of Tokyo.
    3. Ladislav Kristoufek, 2013. "Fractal Markets Hypothesis and the Global Financial Crisis: Wavelet Power Evidence," Papers 1310.1446, arXiv.org.
    4. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2017. "Stability for gains from large investors' strategies in M1/J1 topologies," Papers 1701.02167, arXiv.org, revised Mar 2018.
    5. Li, Da-Ye & Nishimura, Yusaku & Men, Ming, 2014. "Fractal markets: Liquidity and investors on different time horizons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 144-151.
    6. Sergey Lototsky & Henry Schellhorn & Ran Zhao, 2016. "A String Model of Liquidity in Financial Markets," Papers 1608.05900, arXiv.org, revised Apr 2018.
    7. Clarence Simard & Bruno Rémillard, 2019. "Pricing European Options in a Discrete Time Model for the Limit Order Book," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 985-1005, September.
    8. Taiga Saito, 2017. "Hedging and pricing illiquid options with market impacts," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-37, June.
    9. Etienne Chevalier & Vathana Ly Vath & Simone Scotti & Alexandre Roch, 2016. "Optimal Execution Cost For Liquidation Through A Limit Order Market," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-26, February.
    10. Ahmet Umur Ozsoy & Omur Uu{g}ur, 2023. "The QLBS Model within the presence of feedback loops through the impacts of a large trader," Papers 2311.06790, arXiv.org.
    11. Bohumil Stádník & Algita Miečinskienė, 2015. "Complex Model of Market Price Development and its Simulation," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 16(4), pages 786-807, August.
    12. Masaaki Fujii, 2015. "Optimal Position Management for a Market Maker with Stochastic Price Impacts," Papers 1503.07007, arXiv.org, revised Sep 2015.
    13. Panagiotis Christodoulou & Nils Detering & Thilo Meyer-Brandis, 2017. "Local risk-minimization with multiple assets under illiquidity with applications in energy markets," Papers 1705.06918, arXiv.org, revised Jun 2018.
    14. Masaaki Fujii, 2015. "Optimal Position Management for a Market Maker with Stochastic Price Impacts," CARF F-Series CARF-F-360, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2015.
    15. Celeste, Valerio & Corbet, Shaen & Gurdgiev, Constantin, 2020. "Fractal dynamics and wavelet analysis: Deep volatility and return properties of Bitcoin, Ethereum and Ripple," The Quarterly Review of Economics and Finance, Elsevier, vol. 76(C), pages 310-324.

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    More about this item

    Keywords

    Liquidity risk; BSDEs; Stochastic volatility; Price impacts; 60H30; 60G35; 91B24; 91B30; D40; G13;
    All these keywords.

    JEL classification:

    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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