IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v63y1996i1p35-54.html
   My bibliography  Save this article

On martingale measures when asset returns have unpredictable jumps

Author

Listed:
  • Bardhan, Indrajit
  • Chao, Xiuli

Abstract

We study financial market incompleteness induced by discontinuities in asset returns. When there are multiple outcomes for a discontinuity, it is shown that this incompleteness cannot be removed by the introduction of extra securities. Claims cannot be hedged and are thereby not uniquely priced by arbitrage. We characterize the family of martingale measures associated with this form of incompleteness and discuss issues of existence and uniqueness for important special cases. Finally, using methods of stochastic control, we apply these results to derive replicating policies for arbitrary contingent claims and thereby relate the prices of contingent claims to the family of measures.

Suggested Citation

  • Bardhan, Indrajit & Chao, Xiuli, 1996. "On martingale measures when asset returns have unpredictable jumps," Stochastic Processes and their Applications, Elsevier, vol. 63(1), pages 35-54, October.
    • Handle: RePEc:eee:spapps:v:63:y:1996:i:1:p:35-54
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(96)00061-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
    2. 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.
    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
    5. Indrajit Bardhan & Xiuli Chao, 1995. "Martingale Analysis for Assets with Discontinuous Returns," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 243-256, February.
    6. Aase, Knut K., 1988. "Contingent claims valuation when the security price is a combination of an Ito process and a random point process," Stochastic Processes and their Applications, Elsevier, vol. 28(2), pages 185-220, June.
    7. 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.
    8. Bardhan, Indrajit & Chao, Xiulu, 1993. "Pricing options on securities with discontinuous returns," Stochastic Processes and their Applications, Elsevier, vol. 48(1), pages 123-137, October.
    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. Jin, Xing & Zhang, Kun, 2013. "Dynamic optimal portfolio choice in a jump-diffusion model with investment constraints," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1733-1746.
    2. Morten Christensen & Eckhard Platen, 2004. "A General Benchmark Model for Stochastic Jump Sizes," Research Paper Series 139, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Hong, Yi & Jin, Xing, 2018. "Semi-analytical solutions for dynamic portfolio choice in jump-diffusion models and the optimal bond-stock mix," European Journal of Operational Research, Elsevier, vol. 265(1), pages 389-398.
    4. Jérôme Detemple, 2014. "Portfolio Selection: A Review," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 1-21, April.
    5. Ralf Korn & Frank Oertel & Manfred Schäl, 2003. "Notes and Comments: The numeraire portfolio in financial markets modeled by a multi-dimensional jump diffusion process," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 26(2), pages 153-166, November.
    6. Carla Mereu & Robert Stelzer, 2015. "A BSDE arising in an exponential utility maximization problem in a pure jump market model," Papers 1508.07561, arXiv.org, revised Jan 2016.
    7. Anne Eyraud-Loisel, 2005. "Backward stochastic differential equations with enlarged filtration: Option hedging of an insider trader in a financial market with jumps," Post-Print hal-01298905, HAL.
    8. Carverhill, Andrew & Luo, Dan, 2023. "A Bayesian analysis of time-varying jump risk in S&P 500 returns and options," Journal of Financial Markets, Elsevier, vol. 64(C).
    9. Xing Jin & Xudong Zeng, 2018. "Dynamic Asset Allocation with Uncertain Jump Risks: A Pathwise Optimization Approach," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 347-376, May.

    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. Jean-Luc Prigent, 2001. "Option Pricing with a General Marked Point Process," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 50-66, February.
    2. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    3. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Martellini, Lionel, 2005. "Dynamic asset pricing theory with uncertain time-horizon," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1737-1764, October.
    4. Melenberg, B. & Werker, B.J.M., 1996. "On the Pricing of Options in Incomplete Markets," Discussion Paper 1996-19, Tilburg University, Center for Economic Research.
    5. Carolyn W. Chang, 1995. "A No-Arbitrage Martingale Analysis For Jump-Diffusion Valuation," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 18(3), pages 351-381, September.
    6. repec:dau:papers:123456789/5374 is not listed on IDEAS
    7. Bardhan, Indrajit & Chao, Xiuli, 1996. "Stochastic multi-agent equilibria in economies with jump-diffusion uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 361-384.
    8. Melenberg, B. & Werker, B.J.M., 1996. "On the Pricing of Options in Incomplete Markets," Other publications TiSEM 3531d5d5-d0a6-4d54-9d8a-9, Tilburg University, School of Economics and Management.
    9. C. Mancini, 2002. "The European options hedge perfectly in a Poisson-Gaussian stock market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 87-102.
    10. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Working Paper 1159, Economics Department, Queen's University.
    11. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    12. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    13. Christian Gourieroux & Jean Paul Laurent & Huyên Pham, 1998. "Mean‐Variance Hedging and Numéraire," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 179-200, July.
    14. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, Decembrie.
    15. Karl Friedrich Mina & Gerald H. L. Cheang & Carl Chiarella, 2015. "Approximate Hedging Of Options Under Jump-Diffusion Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-26.
    16. Das, Sanjiv Ranjan, 1998. "A direct discrete-time approach to Poisson-Gaussian bond option pricing in the Heath-Jarrow-Morton model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(3), pages 333-369, November.
    17. Ibáñez, Alfredo, 2008. "Factorization of European and American option prices under complete and incomplete markets," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 311-325, February.
    18. Jovanovic, Franck & Schinckus, Christophe, 2016. "Breaking down the barriers between econophysics and financial economics," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 256-266.
    19. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, December.
    20. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    21. Chenghu Ma, 2003. "Term Structure of Interest Rates in the Presence of Levy Jumps: The HJM Approach," Annals of Economics and Finance, Society for AEF, vol. 4(2), pages 401-426, November.

    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:eee:spapps:v:63:y:1996:i:1:p:35-54. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.