IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v249y2016i1p270-280.html
   My bibliography  Save this article

A new elementary geometric approach to option pricing bounds in discrete time models

Author

Listed:
  • Braouezec, Yann
  • Grunspan, Cyril

Abstract

The aim of this paper is to provide a new straightforward measure-free methodology based on convex hulls to determine the no-arbitrage pricing bounds of an option (European or American). The pedagogical interest of our methodology is also briefly discussed. The central result, which is elementary, is presented for a one period model and is subsequently used for multiperiod models. It shows that a certain point, called the forward point, must lie inside a convex polygon. Multiperiod models are then considered and the pricing bounds of a put option (European and American) are explicitly computed. We then show that the barycentric coordinates of the forward point can be interpreted as a martingale pricing measure. An application is provided for the trinomial model where the pricing measure has a simple geometric interpretation in terms of areas of triangles. Finally, we consider the case of entropic barycentric coordinates in a multi asset framework.

Suggested Citation

  • Braouezec, Yann & Grunspan, Cyril, 2016. "A new elementary geometric approach to option pricing bounds in discrete time models," European Journal of Operational Research, Elsevier, vol. 249(1), pages 270-280.
    • Handle: RePEc:eee:ejores:v:249:y:2016:i:1:p:270-280
    DOI: 10.1016/j.ejor.2015.08.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715007614
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.08.024?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. repec:bla:jfinan:v:43:y:1988:i:2:p:301-08 is not listed on IDEAS
    2. Moriggia, V. & Muzzioli, S. & Torricelli, C., 2009. "On the no-arbitrage condition in option implied trees," European Journal of Operational Research, Elsevier, vol. 193(1), pages 212-221, February.
    3. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    4. 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.
    5. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(1), pages 1-12, March.
    6. Geyer, Alois & Hanke, Michael & Weissensteiner, Alex, 2014. "No-arbitrage bounds for financial scenarios," European Journal of Operational Research, Elsevier, vol. 236(2), pages 657-663.
    7. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," The Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    8. Chockalingam, Arun & Muthuraman, Kumar, 2015. "An approximate moving boundary method for American option pricing," European Journal of Operational Research, Elsevier, vol. 240(2), pages 431-438.
    9. Barrieu, Pauline & Scandolo, Giacomo, 2015. "Assessing financial model risk," European Journal of Operational Research, Elsevier, vol. 242(2), pages 546-556.
    10. Jitka Dupačová & Giorgio Consigli & Stein Wallace, 2000. "Scenarios for Multistage Stochastic Programs," Annals of Operations Research, Springer, vol. 100(1), pages 25-53, December.
    11. Ritchken, Peter H, 1985. "On Option Pricing Bounds," Journal of Finance, American Finance Association, vol. 40(4), pages 1219-1233, September.
    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. Alexander Chigodaev, 2016. "Recursive Method for Guaranteed Valuation of Options in Deterministic Game Theoretic Approach," HSE Working papers WP BRP 53/FE/2016, National Research University Higher School of Economics.
    2. Braouezec, Yann & Joliet, Robert, 2019. "Valuing an investment project using no-arbitrage and the alpha-maxmin criteria: From Knightian uncertainty to risk," Economics Letters, Elsevier, vol. 178(C), pages 111-115.
    3. Braouezec, Yann, 2017. "How fundamental is the one-period trinomial model to European option pricing bounds. A new methodological approach," Finance Research Letters, Elsevier, vol. 21(C), pages 92-99.

    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. 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.
    2. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    3. Gambaro, Anna Maria & Kyriakou, Ioannis & Fusai, Gianluca, 2020. "General lattice methods for arithmetic Asian options," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1185-1199.
    4. 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.
    5. 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.
    6. Donald Brown & Rustam Ibragimov & Johan Walden, 2015. "Bounds for path-dependent options," Annals of Finance, Springer, vol. 11(3), pages 433-451, November.
    7. Fabozzi, Frank J. & Paletta, Tommaso & Tunaru, Radu, 2017. "An improved least squares Monte Carlo valuation method based on heteroscedasticity," European Journal of Operational Research, Elsevier, vol. 263(2), pages 698-706.
    8. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.
    9. Fabozzi, Frank J. & Paletta, Tommaso & Stanescu, Silvia & Tunaru, Radu, 2016. "An improved method for pricing and hedging long dated American options," European Journal of Operational Research, Elsevier, vol. 254(2), pages 656-666.
    10. Elyas Elyasiani & Silvia Muzzioli & Alessio Ruggieri, 2016. "Forecasting and pricing powers of option-implied tree models: Tranquil and volatile market conditions," Department of Economics 0099, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    11. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
    12. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
    13. D. Andricopoulos, Ari & Widdicks, Martin & Newton, David P. & Duck, Peter W., 2007. "Extending quadrature methods to value multi-asset and complex path dependent options," Journal of Financial Economics, Elsevier, vol. 83(2), pages 471-499, February.
    14. Gagliardini, Patrick & Ronchetti, Diego, 2013. "Semi-parametric estimation of American option prices," Journal of Econometrics, Elsevier, vol. 173(1), pages 57-82.
    15. Aricson Cruz & José Carlos Dias, 2020. "Valuing American-style options under the CEV model: an integral representation based method," Review of Derivatives Research, Springer, vol. 23(1), pages 63-83, April.
    16. Tianyang Wang & James Dyer & Warren Hahn, 2015. "A copula-based approach for generating lattices," Review of Derivatives Research, Springer, vol. 18(3), pages 263-289, October.
    17. Huimin Yao & Frederik Pretorius, 2014. "Demand Uncertainty, Development Timing and Leasehold Land Valuation: Empirical Testing of Real Options in Residential Real Estate Development," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 42(4), pages 829-868, December.
    18. Nagae, Takeshi & Akamatsu, Takashi, 2008. "A generalized complementarity approach to solving real option problems," Journal of Economic Dynamics and Control, Elsevier, vol. 32(6), pages 1754-1779, June.
    19. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "Nonparametric estimation of American options' exercise boundaries and call prices," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1829-1857, October.
    20. Dabadghao, Shaunak S. & Chockalingam, Arun & Soltani, Taimaz & Fransoo, Jan, 2021. "Valuing Switching options with the moving-boundary method," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).

    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:249:y:2016:i:1:p:270-280. 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.