IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v50y2012i1p50-56.html
   My bibliography  Save this article

Arbitrage in skew Brownian motion models

Author

Listed:
  • Rossello, Damiano

Abstract

Empirical skewness of asset returns can be reproduced by stochastic processes other than the Brownian motion with drift. Some authors have proposed the skew Brownian motion for pricing as well as interest rate modelling. Although the asymmetric feature of random return involved in the stock price process is driven by a parsimonious one-dimensional model, we will show how this is intrinsically incompatible with a modern theory of arbitrage in continuous time. Application to investment performance and to the Black–Scholes pricing model clearly emphasize how this process can provide some kind of arbitrage.

Suggested Citation

  • Rossello, Damiano, 2012. "Arbitrage in skew Brownian motion models," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 50-56.
  • Handle: RePEc:eee:insuma:v:50:y:2012:i:1:p:50-56
    DOI: 10.1016/j.insmatheco.2011.10.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668711001107
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.insmatheco.2011.10.004?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. Marco Frittelli, 2004. "Some Remarks On Arbitrage And Preferences In Securities Market Models," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 351-357, July.
    2. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    3. Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453, World Scientific Publishing Co. Pte. Ltd..
    4. T. R. A. Corns & S. E. Satchell, 2007. "Skew Brownian Motion and Pricing European Options," The European Journal of Finance, Taylor & Francis Journals, vol. 13(6), pages 523-544.
    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. Paolo Pigato, 2019. "Extreme at-the-money skew in a local volatility model," Finance and Stochastics, Springer, vol. 23(4), pages 827-859, October.
    2. Xiaoyang Zhuo & Olivier Menoukeu-Pamen, 2017. "Efficient Piecewise Trees For The Generalized Skew Vasicek Model With Discontinuous Drift," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-34, June.
    3. Hussain, Sultan & Arif, Hifsa & Noorullah, Muhammad & Pantelous, Athanasios A., 2023. "Pricing American Options under Azzalini Ito-McKean Skew Brownian Motions," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    4. Yizhou Bai & Zhiyu Guo, 2019. "An Empirical Investigation to the “Skew” Phenomenon in Stock Index Markets: Evidence from the Nikkei 225 and Others," Sustainability, MDPI, vol. 11(24), pages 1-17, December.
    5. Alexis Anagnostakis, 2023. "Pricing and hedging for a sticky diffusion," Papers 2311.17011, arXiv.org, revised Jan 2024.
    6. Pasricha, Puneet & He, Xin-Jiang, 2022. "Skew-Brownian motion and pricing European exchange options," International Review of Financial Analysis, Elsevier, vol. 82(C).
    7. Antoine Lejay & Paolo Pigato, 2017. "A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data," Working Papers hal-01669082, HAL.
    8. Jun Maeda & Saul D. Jacka, 2017. "An Optimal Stopping Problem Modeling Technical Analysis," Papers 1707.05253, arXiv.org, revised Mar 2020.
    9. Antoine Lejay & Paolo Pigato, 2019. "A Threshold Model For Local Volatility: Evidence Of Leverage And Mean Reversion Effects On Historical Data," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-24, June.

    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. Hong-Ming Yin & Jin Liang & Yuan Wu, 2018. "On a New Corporate Bond Pricing Model with Potential Credit Rating Change and Stochastic Interest Rate," JRFM, MDPI, vol. 11(4), pages 1-12, December.
    2. Augusto Castillo, 2004. "Firm and Corporate Bond Valuation: A Simulation Dynamic Programming Approach," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 41(124), pages 345-360.
    3. SOLNIK, Bruno & COLLIN-DUFRESNE, Pierre, 2000. "On the term structure of default premia in the Swap and Libor markets," HEC Research Papers Series 704, HEC Paris.
    4. Vink, Dennis, 2007. "An Empirical Analysis of Asset-Backed Securitization," MPRA Paper 10382, University Library of Munich, Germany, revised 25 Aug 2008.
    5. Giesecke, Kay & Longstaff, Francis A. & Schaefer, Stephen & Strebulaev, Ilya, 2011. "Corporate bond default risk: A 150-year perspective," Journal of Financial Economics, Elsevier, vol. 102(2), pages 233-250.
    6. Saar, Dan & Yagil, Yossi, 2015. "Forecasting growth and stock performance using government and corporate yield curves: Evidence from the European and Asian markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 37(C), pages 27-41.
    7. 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.
    8. Batten, Jonathan & Hogan, Warren, 2002. "A perspective on credit derivatives," International Review of Financial Analysis, Elsevier, vol. 11(3), pages 251-278.
    9. Jobst, Norbert J. & Zenios, Stavros A., 2005. "On the simulation of portfolios of interest rate and credit risk sensitive securities," European Journal of Operational Research, Elsevier, vol. 161(2), pages 298-324, March.
    10. Esposito, Francesco Paolo, 2011. "Credit risk tools, (numerical methods for finance, university of Limerick 2011)," MPRA Paper 40081, University Library of Munich, Germany.
    11. Dragon Tang & Hong Yan, 2006. "Macroeconomic Conditions, Firm Characteristics, and Credit Spreads," Journal of Financial Services Research, Springer;Western Finance Association, vol. 29(3), pages 177-210, June.
    12. Tingqiang Chen & Suyang Wang, 2023. "Incomplete information model of credit default of micro and small enterprises," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(3), pages 2956-2974, July.
    13. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, March.
    14. Houweling, Patrick & Hoek, Jaap & Kleibergen, Frank, 2001. "The joint estimation of term structures and credit spreads," Journal of Empirical Finance, Elsevier, vol. 8(3), pages 297-323, July.
    15. J. Baixauli & Susana Alvarez, 2012. "Implied Severity Density Estimation: An Extended Semiparametric Method to Compute Credit Value at Risk," Computational Economics, Springer;Society for Computational Economics, vol. 40(2), pages 115-129, August.
    16. Krishnan, C. N. V. & Ritchken, P. H. & Thomson, J. B., 2006. "On Credit-Spread Slopes and Predicting Bank Risk," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(6), pages 1545-1574, September.
    17. Howard Qi & Yan Alice Xie & Sheen Liu, 2010. "Credit Risk Models: An Analysis Of Default Correlation," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 4(1), pages 37-49.
    18. Lando, David & Mortensen, Allan, 2004. "On the Pricing of Step-Up Bonds in the European Telecom Sector," Working Papers 2004-9, Copenhagen Business School, Department of Finance.
    19. Hubner, Georges, 2001. "The analytic pricing of asymmetric defaultable swaps," Journal of Banking & Finance, Elsevier, vol. 25(2), pages 295-316, February.
    20. Liz Dixon-Smith & Roman Goossens & Simon Hayes, 2005. "Default probabilities and expected recovery: an analysis of emerging market sovereign bonds," Bank of England working papers 261, Bank of England.

    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:insuma:v:50:y:2012:i:1:p:50-56. 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/inca/505554 .

    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.