IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v7y2019i3p98-d267950.html
   My bibliography  Save this article

Coherent-Price Systems and Uncertainty-Neutral Valuation

Author

Listed:
  • Patrick Beissner

    (Research School of Economics, Australian National University, Canberra 2601, Australia)

Abstract

This paper considers fundamental questions of arbitrage pricing that arises when the uncertainty model incorporates ambiguity about risk. This additional ambiguity motivates a new principle of risk- and ambiguity-neutral valuation as an extension of the paper by Ross (1976) (Ross, Stephen A. 1976. The arbitrage theory of capital asset pricing. Journal of Economic Theory 13: 341–60). In the spirit of Harrison and Kreps (1979) (Harrison, J. Michael, and David M. Kreps. 1979. Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory 20: 381–408), the paper establishes a micro-economic foundation of viability in which ambiguity-neutrality imposes a fair-pricing principle via symmetric multiple prior martingales. The resulting equivalent symmetric martingale measure set exists if the uncertain volatility in asset prices is driven by an ambiguous Brownian motion.

Suggested Citation

  • Patrick Beissner, 2019. "Coherent-Price Systems and Uncertainty-Neutral Valuation," Risks, MDPI, vol. 7(3), pages 1-18, September.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:3:p:98-:d:267950
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/7/3/98/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/7/3/98/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
    3. Soner, H. Mete & Touzi, Nizar & Zhang, Jianfeng, 2011. "Martingale representation theorem for the G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 265-287, February.
    4. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    5. Marcel Nutz & H. Mete Soner, 2010. "Superhedging and Dynamic Risk Measures under Volatility Uncertainty," Papers 1011.2958, arXiv.org, revised Jun 2012.
    6. repec:dau:papers:123456789/5630 is not listed on IDEAS
    7. Patrick Beissner & Frank Riedel, 2019. "Equilibria Under Knightian Price Uncertainty," Econometrica, Econometric Society, vol. 87(1), pages 37-64, January.
    8. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    10. Epstein, Larry G. & Ji, Shaolin, 2014. "Ambiguous volatility, possibility and utility in continuous time," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 269-282.
    11. Dybvig, Philip H. & Ross, Stephen A., 2003. "Arbitrage, state prices and portfolio theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 10, pages 605-637, Elsevier.
    12. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, May.
    13. Patrick Beissner & Frank Riedel, 2014. "Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Knightian Uncertainty," Papers 1409.6940, arXiv.org.
    14. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
    15. Patrick Beissner, 2017. "Equilibrium prices and trade under ambiguous volatility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(2), pages 213-238, August.
    16. Willard, Gregory A & Dybvig, Philip H, 1999. "Empty Promises and Arbitrage," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 807-834.
    17. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    18. 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.
    19. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    20. Vorbrink, Jörg, 2014. "Financial markets with volatility uncertainty," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 64-78.
    21. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    22. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    23. Rama Cont, 2006. "Model Uncertainty And Its Impact On The Pricing Of Derivative Instruments," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 519-547, July.
    24. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2001. "A Theory of Value with Non-linear Prices: Equilibrium Analysis beyond Vector Lattices," Journal of Economic Theory, Elsevier, vol. 100(1), pages 22-72, September.
    25. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
    26. David Heath & Hyejin Ku, 2006. "Consistency among trading desks," Finance and Stochastics, Springer, vol. 10(3), pages 331-340, September.
    Full references (including those not matched with items on IDEAS)

    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. Matteo Burzoni & Frank Riedel & H. Mete Soner, 2021. "Viability and Arbitrage Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 89(3), pages 1207-1234, May.
    2. Beißner, Patrick, 2013. "Coherent Price Systems and Uncertainty-Neutral Valuation," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 80010, Verein für Socialpolitik / German Economic Association.
    3. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
    4. Patrick Bei{ss}ner, 2012. "Coherent Price Systems and Uncertainty-Neutral Valuation," Papers 1202.6632, arXiv.org.
    5. Weidong Tian & Junya Jiang & Weidong Tian, 2017. "Model Uncertainty Effect on Asset Prices," International Review of Finance, International Review of Finance Ltd., vol. 17(2), pages 205-233, June.
    6. Patrick Beissner & Frank Riedel, 2019. "Equilibria Under Knightian Price Uncertainty," Econometrica, Econometric Society, vol. 87(1), pages 37-64, January.
    7. Romain Blanchard & Laurence Carassus, 2021. "Convergence of utility indifference prices to the superreplication price in a multiple‐priors framework," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 366-398, January.
    8. Marcel Nutz, 2013. "Utility Maximization under Model Uncertainty in Discrete Time," Papers 1307.3597, arXiv.org.
    9. Gonçalo Faria & João Correia-da-Silva, 2012. "The price of risk and ambiguity in an intertemporal general equilibrium model of asset prices," Annals of Finance, Springer, vol. 8(4), pages 507-531, November.
    10. Yuecai Han & Chunyang Liu, 2018. "Asian Option Pricing under Uncertain Volatility Model," Papers 1808.00656, arXiv.org.
    11. Gonçalo Faria & João Correia-da-Silva, 2014. "A closed-form solution for options with ambiguity about stochastic volatility," Review of Derivatives Research, Springer, vol. 17(2), pages 125-159, July.
    12. Dirk Becherer & Klebert Kentia, 2017. "Hedging under generalized good-deal bounds and model uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 171-214, August.
    13. Seokwoo Lee & Alejandro Rivera, 2021. "Extrapolation Bias and Robust Dynamic Liquidity Management," Management Science, INFORMS, vol. 67(10), pages 6421-6442, October.
    14. Vorbrink, Jörg, 2014. "Financial markets with volatility uncertainty," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 64-78.
    15. Romain Blanchard & Laurence Carassus, 2017. "Convergence of utility indifference prices to the superreplication price in a multiple-priors framework," Papers 1709.09465, arXiv.org, revised Oct 2020.
    16. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, August.
    17. Jan Obłój & Johannes Wiesel, 2021. "Distributionally robust portfolio maximization and marginal utility pricing in one period financial markets," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1454-1493, October.
    18. Sebastian Herrmann & Johannes Muhle-Karbe & Frank Thomas Seifried, 2016. "Hedging with Small Uncertainty Aversion," Papers 1605.06429, arXiv.org.
    19. Dirk Becherer & Klebert Kentia, 2016. "Hedging under generalized good-deal bounds and model uncertainty," Papers 1607.04488, arXiv.org, revised Apr 2017.
    20. Sebastian Herrmann & Johannes Muhle-Karbe & Frank Thomas Seifried, 2017. "Hedging with small uncertainty aversion," Finance and Stochastics, Springer, vol. 21(1), pages 1-64, January.

    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:gam:jrisks:v:7:y:2019:i:3:p:98-:d:267950. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.