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Trading volume in models of financial derivatives 

Authors: Sam Howison a; David Lamper a
Affiliation:   a Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, 24-29 St. Giles', Oxford OX1 3LB, UK.
DOI: 10.1080/13504860110074163
Publication Frequency: 6 issues per year
Published in: journal Applied Mathematical Finance, Volume 8, Issue 2 May 2001 , pages 119 - 135
Number of References: 54
Formats available: PDF (English)
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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.
Keywords: Trading Volume; Subordinated Process; Stochastic Volatility; Option Pricing
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