IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v198y2009i2p557-570.html
   My bibliography  Save this article

Third-order extensions of Lo's semiparametric bound for European call options

Author

Listed:
  • Zuluaga, Luis F.
  • Peña, Javier
  • Du, Donglei

Abstract

Computing semiparametric bounds for option prices is a widely studied pricing technique. In contrast to parametric pricing techniques, such as Monte-Carlo simulations, semiparametric pricing techniques do not require strong assumptions about the underlying asset price distribution. We extend classical results in this area. Specifically, we derive closed-form semiparametric bounds for the payoff of a European call option, given up to third-order moment (i.e., mean, variance, and skewness) information on the underlying asset price. We analyze how these bounds tighten the corresponding bounds, when only second-order moment (i.e., mean and variance) information is provided. We describe applications of these results in the context of option pricing; as well as in other areas such as inventory management, and actuarial science.

Suggested Citation

  • Zuluaga, Luis F. & Peña, Javier & Du, Donglei, 2009. "Third-order extensions of Lo's semiparametric bound for European call options," European Journal of Operational Research, Elsevier, vol. 198(2), pages 557-570, October.
    • Handle: RePEc:eee:ejores:v:198:y:2009:i:2:p:557-570
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00768-6
    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. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
    2. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    3. James E. Smith, 1995. "Generalized Chebychev Inequalities: Theory and Applications in Decision Analysis," Operations Research, INFORMS, vol. 43(5), pages 807-825, October.
    4. 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.
    5. Jansen, K. & Haezendonck, J. & Goovaerts, M. J., 1986. "Upper bounds on stop-loss premiums in case of known moments up to the fourth order," Insurance: Mathematics and Economics, Elsevier, vol. 5(4), pages 315-334, October.
    6. Longarela, Iñaki R., 2001. "An Extension of Good-Deal Asset Price Bounds," SSE/EFI Working Paper Series in Economics and Finance 0448, Stockholm School of Economics, revised 19 Oct 2001.
    7. Bruce D. Grundy, "undated". "Option Prices and the Underlying Asset's Return Distribution (Reprint 012)," Rodney L. White Center for Financial Research Working Papers 11-91, Wharton School Rodney L. White Center for Financial Research.
    8. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    9. David Hobson & Peter Laurence & Tai-Ho Wang, 2005. "Static-arbitrage upper bounds for the prices of basket options," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 329-342.
    10. Jinfeng Yue & Bintong Chen & Min-Chiang Wang, 2006. "Expected Value of Distribution Information for the Newsvendor Problem," Operations Research, INFORMS, vol. 54(6), pages 1128-1136, December.
    11. Grundy, R.D., 1991. "Option Prices and the Underlying Asset's Return Distribution," Weiss Center Working Papers 11-91, Wharton School - Weiss Center for International Financial Research.
    12. Ioana Popescu, 2005. "A Semidefinite Programming Approach to Optimal-Moment Bounds for Convex Classes of Distributions," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 632-657, August.
    13. Dimitris Bertsimas & Ioana Popescu, 2002. "On the Relation Between Option and Stock Prices: A Convex Optimization Approach," Operations Research, INFORMS, vol. 50(2), pages 358-374, April.
    14. Levy, Haim, 1985. "Upper and Lower Bounds of Put and Call Option Value: Stochastic Dominance Approach," Journal of Finance, American Finance Association, vol. 40(4), pages 1197-1217, September.
    15. Steftcho P. Dokov & David P. Morton, 2005. "Second-Order Lower Bounds on the Expectation of a Convex Function," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 662-677, August.
    16. Perrakis, Stylianos & Ryan, Peter J, 1984. "Option Pricing Bounds in Discrete Time," Journal of Finance, American Finance Association, vol. 39(2), pages 519-525, June.
    17. Schepper, Ann De & Heijnen, Bart, 2007. "Distribution-free option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 179-199, March.
    18. Ritchken, Peter H, 1985. "On Option Pricing Bounds," Journal of Finance, American Finance Association, vol. 40(4), pages 1219-1233, September.
    19. Lo, Andrew W., 1987. "Semi-parametric upper bounds for option prices and expected payoffs," Journal of Financial Economics, Elsevier, vol. 19(2), pages 373-387, December.
    20. Luis F. Zuluaga & Javier F. Peña, 2005. "A Conic Programming Approach to Generalized Tchebycheff Inequalities," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 369-388, May.
    21. Peter Laurence & Tai-Ho Wang, 2005. "Sharp Upper and Lower Bounds for Basket Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(3), pages 253-282.
    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. Wong, Man Hong & Zhang, Shuzhong, 2013. "Computing best bounds for nonlinear risk measures with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 204-212.
    2. András Prékopa & Anh Ninh & Gabriela Alexe, 2016. "On the relationship between the discrete and continuous bounding moment problems and their numerical solutions," Annals of Operations Research, Springer, vol. 238(1), pages 521-575, March.
    3. Qiaoming Han & Donglei Du & Luis F. Zuluaga, 2014. "Technical Note---A Risk- and Ambiguity-Averse Extension of the Max-Min Newsvendor Order Formula," Operations Research, INFORMS, vol. 62(3), pages 535-542, June.
    4. Karthik Natarajan & Melvyn Sim & Joline Uichanco, 2018. "Asymmetry and Ambiguity in Newsvendor Models," Management Science, INFORMS, vol. 64(7), pages 3146-3167, July.
    5. Marroquı´n-Martı´nez, Naroa & Moreno, Manuel, 2013. "Optimizing bounds on security prices in incomplete markets. Does stochastic volatility specification matter?," European Journal of Operational Research, Elsevier, vol. 225(3), pages 429-442.
    6. András Prékopa & Anh Ninh & Gabriela Alexe, 2016. "On the relationship between the discrete and continuous bounding moment problems and their numerical solutions," Annals of Operations Research, Springer, vol. 238(1), pages 521-575, March.

    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. Hsuan-Chu Lin & Ren-Raw Chen & Oded Palmon, 2012. "Non-parametric method for European option bounds," Review of Quantitative Finance and Accounting, Springer, vol. 38(1), pages 109-129, January.
    2. Laurence, Peter & Wang, Tai-Ho, 2009. "Sharp distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 35-47, February.
    3. Peter Laurence & Tai-Ho Wang, 2008. "Distribution-free upper bounds for spread options and market-implied antimonotonicity gap," The European Journal of Finance, Taylor & Francis Journals, vol. 14(8), pages 717-734.
    4. repec:dau:papers:123456789/30 is not listed on IDEAS
    5. Wong, Man Hong & Zhang, Shuzhong, 2013. "Computing best bounds for nonlinear risk measures with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 204-212.
    6. van Eekelen, Wouter, 2023. "Distributionally robust views on queues and related stochastic models," Other publications TiSEM 9b99fc05-9d68-48eb-ae8c-9, Tilburg University, School of Economics and Management.
    7. Donald J. Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Cowles Foundation Discussion Papers 1518, Cowles Foundation for Research in Economics, Yale University.
    8. Wong, Man Hong & Zhang, Shuzhong, 2014. "On distributional robust probability functions and their computations," European Journal of Operational Research, Elsevier, vol. 233(1), pages 23-33.
    9. Boyle, Phelim P. & Lin, X. Sheldon, 1997. "Bounds on contingent claims based on several assets," Journal of Financial Economics, Elsevier, vol. 46(3), pages 383-400, December.
    10. Schepper, Ann De & Heijnen, Bart, 2007. "Distribution-free option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 179-199, March.
    11. Derek Singh & Shuzhong Zhang, 2020. "Tight Bounds for a Class of Data-Driven Distributionally Robust Risk Measures," Papers 2010.05398, arXiv.org, revised Oct 2020.
    12. Villegas, Andrés M. & Medaglia, Andrés L. & Zuluaga, Luis F., 2012. "Computing bounds on the expected payoff of Alternative Risk Transfer products," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 271-281.
    13. Kirschner, Felix, 2023. "Conic optimization with applications in finance and approximation theory," Other publications TiSEM e9bef4a5-ee46-45be-90d7-9, Tilburg University, School of Economics and Management.
    14. Donald Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Yale School of Management Working Papers amz2581, Yale School of Management, revised 01 Jul 2005.
    15. Robert Howley & Robert Storer & Juan Vera & Luis F. Zuluaga, 2016. "Computing semiparametric bounds on the expected payments of insurance instruments via column generation," Papers 1601.02149, arXiv.org.
    16. Donald Brown & Rustam Ibragimov & Johan Walden, 2015. "Bounds for path-dependent options," Annals of Finance, Springer, vol. 11(3), pages 433-451, November.
    17. Roy H. Kwon & Jonathan Y. Li, 2016. "A stochastic semidefinite programming approach for bounds on option pricing under regime switching," Annals of Operations Research, Springer, vol. 237(1), pages 41-75, February.
    18. Ryan, Peter J., 2003. "Progressive option bounds from the sequence of concurrently expiring options," European Journal of Operational Research, Elsevier, vol. 151(1), pages 193-223, November.
    19. Roy Kwon & Jonathan Li, 2016. "A stochastic semidefinite programming approach for bounds on option pricing under regime switching," Annals of Operations Research, Springer, vol. 237(1), pages 41-75, February.
    20. Didier Henrion & Felix Kirschner & Etienne De Klerk & Milan Korda & Jean-Bernard Lasserre & Victor Magron, 2023. "Revisiting Semidefinite Programming Approaches to Options Pricing: Complexity and Computational Perspectives," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 335-349, March.
    21. Ioana Popescu, 2005. "A Semidefinite Programming Approach to Optimal-Moment Bounds for Convex Classes of Distributions," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 632-657, August.

    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:ejores:v:198:y:2009:i:2:p:557-570. 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/locate/eor .

    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.