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Higher-order volatility

Author

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  • Carey, Alexander

Abstract

An important purpose of derivatives modelling is to provide practitioners with actionable measures of risk. The Black and Scholes volatility remains a favourite on trading floors in spite of well-known biases. One popular extension is to make volatility a function of time and the underlying asset price, as in local volatility models. This paper presents an alternative extension, which produces volatility-like quantities to address the skews and smiles found in most derivatives markets.

Suggested Citation

  • Carey, Alexander, 2005. "Higher-order volatility," MPRA Paper 4993, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:4993
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    File URL: https://mpra.ub.uni-muenchen.de/4993/1/MPRA_paper_4993.pdf
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    References listed on IDEAS

    as
    1. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. 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..
    4. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    5. 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.
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    Cited by:

    1. Carey, Alexander, 2006. "Higher-order volatility: dynamics and sensitivities," MPRA Paper 5009, University Library of Munich, Germany.
    2. Carey, Alexander, 2010. "Higher-order volatility: time series," MPRA Paper 21087, University Library of Munich, Germany.
    3. Carey, Alexander, 2006. "Path-conditional forward volatility," MPRA Paper 4964, University Library of Munich, Germany.

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    More about this item

    Keywords

    higher-order volatility; higher-order moments; volatility smile; S&P 500;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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