| Abstract: |
Modeling the trading volume curves of financial instruments throughout the day
is of key interest in financial trading applications. Predictions of these
so-called volume profiles guide trade execution strategies, for example, a
common strategy is to trade a desired quantity across many orders in line with
the expected volume curve throughout the day so as not to impact the price of
the instrument. The volume curves (for each day) are naturally grouped by
stock and can be further gathered into higher-level groupings, such as by
industry. In order to model such admixtures of volume curves, we introduce a
hierarchical Poisson process model for the intensity functions of admixtures
of inhomogenous Poisson processes, which represent the trading times of the
stock throughout the day. The model is based on the hierarchical Dirichlet
process, and an efficient Markov Chain Monte Carlo (MCMC) algorithm is derived
following the slice sampling framework for Bayesian nonparametric mixture
models. We demonstrate the method on datasets of different stocks from the
Trade and Quote repository maintained by Wharton Research Data Services,
including the most liquid stock on the NASDAQ stock exchange, Apple,
demonstrating the scalability of the approach. |