(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)"> (This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)">
[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/empfin/v11y2004i1p133-161.html
   My bibliography  Save this article

Option pricing with discrete rebalancing

Author

Listed:
  • Prigent, Jean-Luc
  • Renault, Olivier
  • Scaillet, Olivier
Abstract
We consider option pricing when dynamic portfolios are discretely rebalanced. The portfolio adjustments only occur after fixed relative variation of the stock price. The stock price follows a marked point process and the market is incomplete. We first characterize the equivalent martingale measures. An explicit formula based on the minimal martingale measure is then provided together with the hedging strategy underlying portfolio adjustments. Under adequate conditions on the stock price dynamics, the minimal pricing formula converges to the Black-Scholes formula when the triggering price increment shrinks to zero. This is shown theoretically and numerically on two examples : a marked Poisson process and a jump process driven by a latent geometric Brownian motion. For the empirical application we use IBM intraday transaction data and compare option prices given by the marked Poisson model and the Black-Scholes model.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Prigent, Jean-Luc & Renault, Olivier & Scaillet, Olivier, 2004. "Option pricing with discrete rebalancing," Journal of Empirical Finance, Elsevier, vol. 11(1), pages 133-161, January.
    • Handle: RePEc:eee:empfin:v:11:y:2004:i:1:p:133-161
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0927-5398(03)00043-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Laurent, J.P. & Scaillet, O., 1997. "Variance Optimal Cap Pricing Models," LIDAM Discussion Papers IRES 1999002, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES), revised 01 Jan 1999.
    2. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187, July.
    3. Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 1999. "An Autoregressive Conditional Binomial Option Pricing Model," Working Papers 99-65, Center for Research in Economics and Statistics.
    4. David B. Colwell & Robert J. Elliott, 1993. "Discontinuous Asset Prices And Non‐Attainable Contingent Claims1," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 295-308, July.
    5. Fabio Mercurio & Ton Vorst, 1996. "Option pricing with hedging at fixed trading dates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(2), pages 135-158.
    6. 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..
    7. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-664, May.
    8. Jean-Luc Prigent, 1999. "Incomplete markets: convergence of options values under the minimal martingale measure," Post-Print hal-03679524, HAL.
    9. Engle, Robert F. & Russell, Jeffrey R., 1997. "Forecasting the frequency of changes in quoted foreign exchange prices with the autoregressive conditional duration model," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 187-212, June.
    10. J. L. Prigent, 1997. "Incomplete markets : Convergence of options values under the minimal martingale measure. The multidimensional case," THEMA Working Papers 97-35, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    11. Schweizer, Martin, 1992. "Martingale densities for general asset prices," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 363-378.
    12. Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298, October.
    13. O. Scaillet & J.-L. Prigent & J.-P. Lesne, 2000. "Convergence of discrete time option pricing models under stochastic interest rates," Finance and Stochastics, Springer, vol. 4(1), pages 81-93.
    14. Bouleau, Nicolas & Lamberton, Damien, 1989. "Residual risks and hedging strategies in Markovian markets," Stochastic Processes and their Applications, Elsevier, vol. 33(1), pages 131-150, October.
    15. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
    16. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
    17. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    18. 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.
    19. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    20. 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.
    21. repec:crs:wpaper:9932 is not listed on IDEAS
    22. Hua He & William P. Keirstead & Joachim Rebholz, 1998. "Double Lookbacks," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 201-228, July.
    23. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    24. repec:bla:jfinan:v:53:y:1998:i:6:p:2059-2106 is not listed on IDEAS
    25. Chesher, Andrew & Dhaene, Geert & Gouriéroux, Christian & Scaillet, Olivier, 1999. "Bartlett Identities Tests," LIDAM Discussion Papers IRES 1999019, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    26. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, 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. J.L. Prigent & O. Scaillet, 2000. "Weak Convergence of Hedging Strategies of Contingent Claims," THEMA Working Papers 2000-50, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    2. Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 1999. "An Autoregressive Conditional Binomial Option Pricing Model," Working Papers 99-65, Center for Research in Economics and Statistics.
    3. Cheng Cai & Tiziano De Angelis & Jan Palczewski, 2020. "Optimal hedging of a perpetual American put with a single trade," Papers 2003.06249, arXiv.org, revised Sep 2020.

    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 & Olivier Renault & Olivier Scaillet, 1999. "An Autoregressive Conditional Binomial Option Pricing Model," Working Papers 99-65, Center for Research in Economics and Statistics.
    2. repec:dau:papers:123456789/5374 is not listed on IDEAS
    3. Jean-Luc Prigent, 2001. "Option Pricing with a General Marked Point Process," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 50-66, February.
    4. Duffie, Darrell, 2003. "Intertemporal asset pricing 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 11, pages 639-742, Elsevier.
    5. Møller, T., 2002. "On Valuation and Risk Management at the Interface of Insurance and Finance," British Actuarial Journal, Cambridge University Press, vol. 8(4), pages 787-827, October.
    6. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    7. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, August.
    8. W. Schachermayer, 1994. "Martingale Measures For Discrete‐Time Processes With Infinite Horizon," Mathematical Finance, Wiley Blackwell, vol. 4(1), pages 25-55, January.
    9. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    10. 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.
    11. A Craig Burnside & Jeremy J Graveline, 2020. "On the Asset Market View of Exchange Rates," The Review of Financial Studies, Society for Financial Studies, vol. 33(1), pages 239-260.
    12. Marc Atlan & Hélyette Geman & Dilip Madan & Marc Yor, 2007. "Correlation and the pricing of risks," Annals of Finance, Springer, vol. 3(4), pages 411-453, October.
    13. Mark Broadie & Jérôme Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
    14. Davide Lauria & W. Brent Lindquist & Svetlozar T. Rachev & Yuan Hu, 2023. "Unifying Market Microstructure and Dynamic Asset Pricing," Papers 2304.02356, arXiv.org, revised Feb 2024.
    15. Mark Mink & Frans J. de Weert, 2022. "Black-Scholes-Merton Option Pricing Revisited: Did we Find a Fatal Flaw?," Papers 2202.05671, arXiv.org, revised Oct 2024.
    16. Paola Zerilli, 2005. "Option pricing and spikes in volatility: theoretical and empirical analysis," Money Macro and Finance (MMF) Research Group Conference 2005 76, Money Macro and Finance Research Group.
    17. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2, July-Dece.
    18. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, May.
    19. Munk, Claus, 2015. "Financial Asset Pricing Theory," OUP Catalogue, Oxford University Press, number 9780198716457.
    20. Protter, Philip, 2001. "A partial introduction to financial asset pricing theory," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 169-203, February.
    21. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.

    More about this item

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    Statistics

    Access and download statistics

    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:empfin:v:11:y:2004:i:1:p:133-161. 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/jempfin .

    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.