IDEAS home Printed from https://ideas.repec.org/p/sce/scecfa/54.html
   My bibliography  Save this paper

A closed form approach to valuing and hedging basket options

Author

Listed:
  • Svetlana Borovkova

    () (Delft Institute of Applied Mathematics Delft University of Technology)

  • Ferry Permana

    (Delft University of Technology)

Abstract

We develop a new approach to valuing and hedging basket options. We consider baskets of assets with potentially negative portfolio weights (spread options are a subclass of such basket options). The basket distribution is approximated using a generalized family of log-normal distributions. This approximation copes with negative basket values as well as negative skewness of the basket distribution, and it provides closed formulae for the option price and greeks. Numerical simulations show our approach provides a very close approximation of the option price, and performs remarkably well in terms of the hedging error. We analyze the option price sensitivities with respect to the assets' volatilities and correlations; and explain the seemingly paradoxical phenomenon of negative volatility vegas

Suggested Citation

  • Svetlana Borovkova & Ferry Permana, 2006. "A closed form approach to valuing and hedging basket options," Computing in Economics and Finance 2006 54, Society for Computational Economics.
  • Handle: RePEc:sce:scecfa:54
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    References listed on IDEAS

    as
    1. William A. Barnett & Shu Wu, 2011. "On User Costs of Risky Monetary Assets," World Scientific Book Chapters,in: Financial Aggregation And Index Number Theory, chapter 3, pages 85-105 World Scientific Publishing Co. Pte. Ltd..
    2. repec:wsi:gjexxx:v:01:y:2012:i:01:n:s225136121250005x is not listed on IDEAS
    3. Schunk, Donald L, 2001. "The Relative Forecasting Performance of the Divisia and Simple Sum Monetary Aggregates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 33(2), pages 272-283, May.
    4. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 25-38, January.
    5. William Barnett & Apostolos Serletis & W. Erwin Diewert, 2005. "The Theory of Monetary Aggregation (book front matter)," Macroeconomics 0511008, EconWPA.
    6. Rotemberg, Julio J & Driscoll, John C & Poterba, James M, 1995. "Money, Output, and Prices: Evidence from a New Monetary Aggregate," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 67-83, January.
    7. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1983. "Forecasting and Conditional Projection Using Realistic Prior Distributions," NBER Working Papers 1202, National Bureau of Economic Research, Inc.
    8. William Barnett, 2005. "Monetary Aggregation," Macroeconomics 0503017, EconWPA.
    9. William A Barnett & Unja Chae & John W Keating, 2012. "Forecast Design In Monetary Capital Stock Measurement," Global Journal of Economics (GJE), World Scientific Publishing Co. Pte. Ltd., pages 1-53.
    10. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    11. Hoover, Kevin D. & Perez, Stephen J., 1994. "Post hoc ergo propter once more an evaluation of 'does monetary policy matter?' in the spirit of James Tobin," Journal of Monetary Economics, Elsevier, vol. 34(1), pages 47-74, August.
    12. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    13. Barnett, William A., 1978. "The user cost of money," Economics Letters, Elsevier, vol. 1(2), pages 145-149.
    14. Keating, John W., 2000. "Macroeconomic Modeling with Asymmetric Vector Autoregressions," Journal of Macroeconomics, Elsevier, vol. 22(1), pages 1-28, January.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    basket options; log-normal approximation; closed formula; hedging; greeks; correlation; vega risk;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    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:sce:scecfa:54. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/sceeeea.html .

    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.

    We have no references for this item. You can help adding them by using 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.