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Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices

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  • Tomasz R. Bielecki
  • Igor Cialenco
  • Ismail Iyigunler
  • Rodrigo Rodriguez

Abstract

In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of Asset Pricing using the dynamic coherent risk measures. We introduce the dynamic ask and bid prices of a derivative contract in markets with transaction costs. Based on these results, we derive a representation theorem for the dynamic bid and ask prices in terms of dynamically consistent sequence of sets of probability measures and risk-neutral measures. To illustrate our results, we compute the ask and bid prices of some path-dependent options using the dynamic Gain-Loss Ratio.

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  • Tomasz R. Bielecki & Igor Cialenco & Ismail Iyigunler & Rodrigo Rodriguez, 2012. "Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices," Papers 1205.4790, arXiv.org, revised Jun 2013.
    • Handle: RePEc:arx:papers:1205.4790
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    References listed on IDEAS

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    1. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    2. 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.
    3. Alexander Cherny, 2007. "Pricing and hedging European options with discrete-time coherent risk," Finance and Stochastics, Springer, vol. 11(4), pages 537-569, October.
    4. repec:dau:papers:123456789/5630 is not listed on IDEAS
    5. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    6. Jeremy Staum, 2004. "Fundamental Theorems of Asset Pricing for Good Deal Bounds," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 141-161, April.
    7. Alexander S. Cherny & Dilip B. Madan, 2006. "Pricing and hedging in incomplete markets with coherent risk," Papers math/0605064, arXiv.org.
    8. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48, January.
    9. Stefan Jaschke & Uwe Küchler, 2001. "Coherent risk measures and good-deal bounds," Finance and Stochastics, Springer, vol. 5(2), pages 181-200.
    10. Tomasz R. Bielecki & Igor Cialenco & Zhao Zhang, 2010. "Dynamic Coherent Acceptability Indices and their Applications to Finance," Papers 1010.4339, arXiv.org, revised May 2011.
    11. 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.
    12. Berend Roorda & J. M. Schumacher & Jacob Engwerda, 2005. "Coherent Acceptability Measures In Multiperiod Models," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 589-612, October.
    13. Alexander S. Cherny, 2006. "Pricing with coherent risk," Papers math/0605049, arXiv.org.
    14. J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, vol. 2(3), pages 259-273.
    15. PInar, Mustafa Ç. & Salih, AslIhan & CamcI, Ahmet, 2010. "Expected gain-loss pricing and hedging of contingent claims in incomplete markets by linear programming," European Journal of Operational Research, Elsevier, vol. 201(3), pages 770-785, March.
    16. Takuji Arai & Masaaki Fukasawa, 2011. "Convex risk measures for good deal bounds," Papers 1108.1273, arXiv.org.
    17. repec:crs:wpaper:9513 is not listed on IDEAS
    18. Schachermayer, W., 1992. "A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 249-257, December.
    19. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    20. 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.
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    Citations

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    Cited by:

    1. Matteo Michielon & Asma Khedher & Peter Spreij, 2021. "Liquidity-free implied volatilities: an approach using conic finance," Papers 2110.11718, arXiv.org.
    2. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2016. "A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective," Papers 1603.09030, arXiv.org, revised Jan 2017.
    3. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    4. Qi Feng & Man Luo & Zhaoyu Zhang, 2021. "Deep Signature FBSDE Algorithm," Papers 2108.10504, arXiv.org, revised Aug 2022.
    5. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2018. "A Unified Approach to Time Consistency of Dynamic Risk Measures and Dynamic Performance Measures in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 204-221, February.
    6. Erhan Bayraktar & Gu Wang, 2018. "Quantile Hedging in a semi-static market with model uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(2), pages 197-227, April.
    7. 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.
    8. Dilip B. Madan, 2016. "Conic Portfolio Theory," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-42, May.
    9. Marcin Pitera & Mikl'os R'asonyi, 2023. "Utility-based acceptability indices," Papers 2310.02014, arXiv.org.
    10. Tomasz R. Bielecki & Igor Cialenco & Tao Chen, 2014. "Dynamic Conic Finance via Backward Stochastic Difference Equations," Papers 1412.6459, arXiv.org, revised Dec 2014.
    11. Biagini, Sara & Bion-Nadal, Jocelyne, 2014. "Dynamic quasi concave performance measures," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 143-153.
    12. Marcelo Brutti Righi, 2021. "Star-shaped acceptability indexes," Papers 2110.08630, arXiv.org, revised Jun 2022.

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