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Trading volume in models of financial derivatives

Author

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  • Sam Howison
  • David Lamper

Abstract

This paper develops a subordinated stochastic process model for an asset price, where the directing process is identified as information. Motivated by recent empirical and theoretical work, the paper makes use of the under-used market statistic of transaction count as a suitable proxy for the information flow. An option pricing formula is derived, and comparisons with stochastic volatility models are drawn. Both the asset price and the number of trades are used in parameter estimation. The underlying process is found to be fast mean reverting, and this is exploited to perform an asymptotic expansion. The implied volatility skew is then used to calibrate the model.

Suggested Citation

  • Sam Howison & David Lamper, 2001. "Trading volume in models of financial derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(2), pages 119-135.
    • Handle: RePEc:taf:apmtfi:v:8:y:2001:i:2:p:119-135
    DOI: 10.1080/13504860110074163
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    References listed on IDEAS

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    1. Leonenko, N.N. & Petherick, S. & Sikorskii, A., 2012. "A normal inverse Gaussian model for a risky asset with dependence," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 109-115.
    2. Emanuel Derman, 2002. "The perception of time, risk and return during periods of speculation," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 282-296.
    3. Emanuel Derman, 2002. "The Perception of Time, Risk and Return During Periods of Speculation," Papers cond-mat/0201345, arXiv.org.
    4. Cheuathonghua, Massaporn & Padungsaksawasdi, Chaiyuth, 2024. "The volume-implied volatility relation in financial markets: A behavioral explanation," The North American Journal of Economics and Finance, Elsevier, vol. 71(C).

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