IDEAS home Printed from https://ideas.repec.org/p/hhb/aarbfi/2009-05.html
   My bibliography  Save this paper

A Consistent Pricing Model for Index Options and Volatility Derivatives

Author

Listed:
  • Cont, Rama

    () (Center for Financial Engineering)

  • Kokholm, Thomas

    () (Department of Business Studies, Aarhus School of Business)

Abstract

We propose and study a flexible modeling framework for the joint dynamics of an index and a set of forward variance swap rates written on this index, allowing options on forward variance swaps and options on the underlying index to be priced consistently. Our model reproduces various empirically observed properties of variance swap dynamics and allows for jumps in volatility and returns. An affine specification using L´evy processes as building blocks leads to analytically tractable pricing formulas for options on variance swaps as well as efficient numerical methods for pricing of European options on the underlying asset. The model has the convenient feature of decoupling the vanilla skews from spot/volatility correlations and allowing for different conditional correlations in large and small spot/volatility moves. We show that our model can simultaneously fit prices of European options on S&P 500 across strikes and maturities as well as options on the VIX volatility index. The calibration of the model is done in two steps, first by matching VIX option prices and then by matching prices of options on the underlying

Suggested Citation

  • Cont, Rama & Kokholm, Thomas, 2009. "A Consistent Pricing Model for Index Options and Volatility Derivatives," Finance Research Group Working Papers F-2009-05, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  • Handle: RePEc:hhb:aarbfi:2009-05
    as

    Download full text from publisher

    File URL: http://www.hha.dk/afl/wp/fin/F_2009_05.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Sheridan Titman & Sergey Tsyplakov, 2007. "A Dynamic Model of Optimal Capital Structure," Review of Finance, European Finance Association, pages 401-451.
    2. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    3. Egami, Masahiko, 2009. "A framework for the study of expansion options, loan commitments and agency costs," Journal of Corporate Finance, Elsevier, vol. 15(3), pages 345-357, June.
    4. Lyandres, Evgeny & Zhdanov, Alexei, 2010. "Accelerated investment effect of risky debt," Journal of Banking & Finance, Elsevier, vol. 34(11), pages 2587-2599, November.
    5. Cleary, Sean & Povel, Paul & Raith, Michael, 2007. "The U-Shaped Investment Curve: Theory and Evidence," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(01), pages 1-39, March.
    6. Jensen, Michael C. & Meckling, William H., 1976. "Theory of the firm: Managerial behavior, agency costs and ownership structure," Journal of Financial Economics, Elsevier, vol. 3(4), pages 305-360, October.
    7. Firth, Michael & Lin, Chen & Wong, Sonia M.L., 2008. "Leverage and investment under a state-owned bank lending environment: Evidence from China," Journal of Corporate Finance, Elsevier, vol. 14(5), pages 642-653, December.
    8. Mauer, David C. & Sarkar, Sudipto, 2005. "Real options, agency conflicts, and optimal capital structure," Journal of Banking & Finance, Elsevier, vol. 29(6), pages 1405-1428, June.
    9. Jan Ericsson & Joel Reneby, 1998. "A framework for valuing corporate securities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(3-4), pages 143-163.
    10. Heitor Almeida & Murillo Campello & Michael S. Weisbach, 2004. "The Cash Flow Sensitivity of Cash," Journal of Finance, American Finance Association, vol. 59(4), pages 1777-1804, August.
    11. Hayne E. Leland., 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Research Program in Finance Working Papers RPF-233, University of California at Berkeley.
    12. Jensen, Michael C, 1986. "Agency Costs of Free Cash Flow, Corporate Finance, and Takeovers," American Economic Review, American Economic Association, vol. 76(2), pages 323-329, May.
    13. Andrea Gamba & Alexander Triantis, 2008. "The Value of Financial Flexibility," Journal of Finance, American Finance Association, vol. 63(5), pages 2263-2296, October.
    14. Opler, Tim & Pinkowitz, Lee & Stulz, Rene & Williamson, Rohan, 1999. "The determinants and implications of corporate cash holdings," Journal of Financial Economics, Elsevier, vol. 52(1), pages 3-46, April.
    15. Hayne E. Leland, 1998. "Agency Costs, Risk Management, and Capital Structure," Journal of Finance, American Finance Association, vol. 53(4), pages 1213-1243, August.
    16. Matthew T. Billett & Tao-Hsien Dolly King & David C. Mauer, 2007. "Growth Opportunities and the Choice of Leverage, Debt Maturity, and Covenants," Journal of Finance, American Finance Association, vol. 62(2), pages 697-730, April.
    17. Glenn W. Boyle & Graeme A. Guthrie, 2003. "Investment, Uncertainty, and Liquidity," Journal of Finance, American Finance Association, vol. 58(5), pages 2143-2166, October.
    18. Myers, Stewart C., 1977. "Determinants of corporate borrowing," Journal of Financial Economics, Elsevier, vol. 5(2), pages 147-175, November.
    19. Lyandres, Evgeny, 2007. "Costly external financing, investment timing, and investment-cash flow sensitivity," Journal of Corporate Finance, Elsevier, vol. 13(5), pages 959-980, December.
    20. Dirk Hackbarth & David C. Mauer, 2012. "Optimal Priority Structure, Capital Structure, and Investment," Review of Financial Studies, Society for Financial Studies, vol. 25(3), pages 747-796.
    21. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474, June.
    22. Bryan, Stephen & Nash, Robert & Patel, Ajay, 2006. "Can the agency costs of debt and equity explain the changes in executive compensation during the 1990s?," Journal of Corporate Finance, Elsevier, vol. 12(3), pages 516-535, June.
    23. Leland, Hayne E, 1994. " Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-1252, September.
    24. Michael Faulkender & Rong Wang, 2006. "Corporate Financial Policy and the Value of Cash," Journal of Finance, American Finance Association, vol. 61(4), pages 1957-1990, August.
    25. Moyen, Nathalie, 2007. "How big is the debt overhang problem?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 433-472, February.
    26. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
    27. Christopher A. Hennessy, 2004. "Tobin's "Q", Debt Overhang, and Investment," Journal of Finance, American Finance Association, vol. 59(4), pages 1717-1742, August.
    28. Childs, Paul D. & Mauer, David C. & Ott, Steven H., 2005. "Interactions of corporate financing and investment decisions: The effects of agency conflicts," Journal of Financial Economics, Elsevier, vol. 76(3), pages 667-690, June.
    29. Parrino, Robert & Weisbach, Michael S., 1999. "Measuring investment distortions arising from stockholder-bondholder conflicts," Journal of Financial Economics, Elsevier, vol. 53(1), pages 3-42, July.
    30. Aivazian, Varouj A. & Ge, Ying & Qiu, Jiaping, 2005. "The impact of leverage on firm investment: Canadian evidence," Journal of Corporate Finance, Elsevier, vol. 11(1-2), pages 277-291, March.
    31. Mello, Antonio S & Parsons, John E, 1992. " Measuring the Agency Cost of Debt," Journal of Finance, American Finance Association, vol. 47(5), pages 1887-1904, December.
    32. Thomas W. Bates, 2005. "Asset Sales, Investment Opportunities, and the Use of Proceeds," Journal of Finance, American Finance Association, vol. 60(1), pages 105-135, February.
    33. Morellec, Erwan, 2001. "Asset liquidity, capital structure, and secured debt," Journal of Financial Economics, Elsevier, vol. 61(2), pages 173-206, August.
    34. Nash, Robert C. & Netter, Jeffry M. & Poulsen, Annette B., 2003. "Determinants of contractual relations between shareholders and bondholders: investment opportunities and restrictive covenants," Journal of Corporate Finance, Elsevier, vol. 9(2), pages 201-232, March.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    No keywords;

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hhb:aarbfi:2009-05. 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: (Helle Vinbaek Stenholt). General contact details of provider: http://edirc.repec.org/data/ifhhadk.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.