IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v22y2018i2d10.1007_s00780-017-0352-4.html
   My bibliography  Save this article

Perfect hedging under endogenous permanent market impacts

Author

Listed:
  • Masaaki Fukasawa

    (Osaka University)

  • Mitja Stadje

    (Ulm University)

Abstract

We model a nonlinear price curve quoted in a market as the utility indifference curve of a representative liquidity supplier. As the utility function, we adopt a g $g$ -expectation. In contrast to the standard framework of financial engineering, a trader is no longer a price taker as any trade has a permanent market impact via an effect on the supplier’s inventory. The P&L of a trading strategy is written as a nonlinear stochastic integral. Under this market impact model, we introduce a completeness condition under which any derivative can be perfectly replicated by a dynamic trading strategy. In the special case of a Markovian setting, the corresponding pricing and hedging can be done by solving a semilinear PDE.

Suggested Citation

  • Masaaki Fukasawa & Mitja Stadje, 2018. "Perfect hedging under endogenous permanent market impacts," Finance and Stochastics, Springer, vol. 22(2), pages 417-442, April.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:2:d:10.1007_s00780-017-0352-4
    DOI: 10.1007/s00780-017-0352-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-017-0352-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00780-017-0352-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Olivier Guéant & Jiang Pu, 2017. "Option Pricing And Hedging With Execution Costs And Market Impact," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 803-831, July.
    2. Freddy Delbaen & Shige Peng & Emanuela Rosazza Gianin, 2010. "Representation of the penalty term of dynamic concave utilities," Finance and Stochastics, Springer, vol. 14(3), pages 449-472, September.
    3. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    4. Brennan, Michael J & Schwartz, Eduardo S, 1989. "Portfolio Insurance and Financial Market Equilibrium," The Journal of Business, University of Chicago Press, vol. 62(4), pages 455-472, October.
    5. ,, 2016. "Objective rationality and uncertainty averse preferences," Theoretical Economics, Econometric Society, vol. 11(2), May.
    6. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    7. Ulrich Horst & Traian A. Pirvu & Gonçalo Dos Reis, 2010. "On Securitization, Market Completion and Equilibrium Risk Transfer," SFB 649 Discussion Papers SFB649DP2010-010, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Tomas Björk & Irina Slinko, 2006. "Towards a General Theory of Good-Deal Bounds," Review of Finance, European Finance Association, vol. 10(2), pages 221-260.
    9. Glosten, Lawrence R. & Milgrom, Paul R., 1985. "Bid, ask and transaction prices in a specialist market with heterogeneously informed traders," Journal of Financial Economics, Elsevier, vol. 14(1), pages 71-100, March.
    10. Ho, Thomas & Stoll, Hans R., 1981. "Optimal dealer pricing under transactions and return uncertainty," Journal of Financial Economics, Elsevier, vol. 9(1), pages 47-73, March.
    11. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    13. Bence Toth & Zoltan Eisler & Jean-Philippe Bouchaud, 2016. "The square-root impact law also holds for option markets," Papers 1602.03043, arXiv.org.
    14. Patrick Cheridito & Freddy Delbaen & Michael Kupper, 2006. "Coherent and convex monetary risk measures for unbounded càdlàg processes," Finance and Stochastics, Springer, vol. 10(3), pages 427-448, September.
    15. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, April.
    16. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    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, January.
    18. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    19. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Conditional Risk Mappings," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 544-561, August.
    20. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374, October.
    21. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
    22. Barrieu, Pauline & El Karoui, Nicole, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.
    23. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    24. Peter Bank & Dmitry Kramkov, 2015. "A model for a large investor trading at market indifference prices. I: Single-period case," Finance and Stochastics, Springer, vol. 19(2), pages 449-472, April.
    25. Susanne Klöppel & Martin Schweizer, 2007. "Dynamic Indifference Valuation Via Convex Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 599-627, October.
    26. Masaaki Fukasawa, 2014. "Efficient discretization of stochastic integrals," Finance and Stochastics, Springer, vol. 18(1), pages 175-208, January.
    27. Dilip B. Madan & Alexander Cherny, 2010. "Markets As A Counterparty: An Introduction To Conic Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1149-1177.
    28. Alexander Cherny & Dilip Madan, 2009. "New Measures for Performance Evaluation," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2371-2406, July.
    29. Peter Bank & Dmitry Kramkov, 2011. "A model for a large investor trading at market indifference prices. II: Continuous-time case," Papers 1110.3229, arXiv.org, revised Sep 2015.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2021. "Optimal investment, derivative demand, and arbitrage under price impact," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 3-35, January.
    2. Thai Nguyen & Mitja Stadje, 2020. "Utility maximization under endogenous pricing," Papers 2005.04312, arXiv.org, revised Mar 2024.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Masaaki Fukasawa & Mitja Stadje, 2017. "Perfect hedging under endogenous permanent market impacts," Papers 1702.01385, arXiv.org.
    2. Bellini, Fabio & Laeven, Roger J.A. & Rosazza Gianin, Emanuela, 2021. "Dynamic robust Orlicz premia and Haezendonck–Goovaerts risk measures," European Journal of Operational Research, Elsevier, vol. 291(2), pages 438-446.
    3. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2021. "Optimal investment, derivative demand, and arbitrage under price impact," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 3-35, January.
    4. Mitja Stadje, 2018. "Representation Results for Law Invariant Recursive Dynamic Deviation Measures and Risk Sharing," Papers 1811.09615, arXiv.org, revised Dec 2018.
    5. Bion-Nadal, Jocelyne, 2009. "Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 738-750, December.
    6. Volker Krätschmer & Marcel Ladkau & Roger J. A. Laeven & John G. M. Schoenmakers & Mitja Stadje, 2018. "Optimal Stopping Under Uncertainty in Drift and Jump Intensity," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1177-1209, November.
    7. Roger J. A. Laeven & Mitja Stadje, 2013. "Entropy Coherent and Entropy Convex Measures of Risk," Mathematics of Operations Research, INFORMS, vol. 38(2), pages 265-293, May.
    8. Ji, Ronglin & Shi, Xuejun & Wang, Shijie & Zhou, Jinming, 2019. "Dynamic risk measures for processes via backward stochastic differential equations," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 43-50.
    9. Zachary Feinstein & Birgit Rudloff, 2018. "Scalar multivariate risk measures with a single eligible asset," Papers 1807.10694, arXiv.org, revised Feb 2021.
    10. Thai Nguyen & Mitja Stadje, 2020. "Utility maximization under endogenous pricing," Papers 2005.04312, arXiv.org, revised Mar 2024.
    11. Dan A. Iancu & Marek Petrik & Dharmashankar Subramanian, 2015. "Tight Approximations of Dynamic Risk Measures," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 655-682, March.
    12. Jocelyne Bion-Nadal, 2007. "Bid-Ask Dynamic Pricing in Financial Markets with Transaction Costs and Liquidity Risk," Papers math/0703074, arXiv.org.
    13. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2018. "Optimal Investment, Demand and Arbitrage under Price Impact," Papers 1804.09151, arXiv.org, revised Dec 2018.
    14. Masaaki Fukasawa, 2014. "Efficient price dynamics in a limit order market: an utility indifference approach," Papers 1410.8224, arXiv.org.
    15. Knispel, Thomas & Laeven, Roger J.A. & Svindland, Gregor, 2016. "Robust optimal risk sharing and risk premia in expanding pools," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 182-195.
    16. Roorda, Berend & Schumacher, J.M., 2011. "The strictest common relaxation of a family of risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 29-34, January.
    17. Sigrid Källblad, 2017. "Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals," Finance and Stochastics, Springer, vol. 21(2), pages 397-425, April.
    18. Dilip Madan, 2015. "Asset pricing theory for two price economies," Annals of Finance, Springer, vol. 11(1), pages 1-35, February.
    19. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2014. "A unified approach to time consistency of dynamic risk measures and dynamic performance measures in discrete time," Papers 1409.7028, arXiv.org, revised Sep 2017.
    20. Roorda Berend & Schumacher Hans, 2013. "Membership conditions for consistent families of monetary valuations," Statistics & Risk Modeling, De Gruyter, vol. 30(3), pages 255-280, August.

    More about this item

    Keywords

    Nonlinear stochastic integral; g $g$ -Expectation; Market impact;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:finsto:v:22:y:2018:i:2:d:10.1007_s00780-017-0352-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.