Trading Volume in Models
of Financial DerivativesSam Howison, David
lamper
Abstract
This paper develops a subordinated stochastic process
model for the asset price, where the directing process is identified as
information. Motivated by recent empirical and theoretical work, we make 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 this model.
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