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Nonrandom price movements

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  • Madan, Dilip B.
  • Wang, King

Abstract

Local peaks and valleys are constructed as time points with prices respectively above and below the two adjacent values. We demonstrate, quite generally, that under stylized financial model assumptions, the expected inter peak and inter valley times should be 4 days. The times observed in data are statistically significantly below this value, possibly questioning stylized assumptions. Our investigation thereby lends some support to the presence of mean reversion and the related activities of technical and algorithmic traders seeking to benefit from such a structure.

Suggested Citation

  • Madan, Dilip B. & Wang, King, 2016. "Nonrandom price movements," Finance Research Letters, Elsevier, vol. 17(C), pages 103-109.
    • Handle: RePEc:eee:finlet:v:17:y:2016:i:c:p:103-109
    DOI: 10.1016/j.frl.2016.02.003
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    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. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    6. 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.
    7. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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    Cited by:

    1. Madan, Dilip B. & Wang, King, 2021. "The structure of financial returns," Finance Research Letters, Elsevier, vol. 40(C).

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    More about this item

    Keywords

    Variance gamma; Geometric Brownian motion; Momentum; Mean reversion;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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