Mathematical Finance Seminar
February 9, 2012 5:30 PM to 7:00 PM
Alan de Genaro Dario, CIMS and BM&F Bovespa
Point Processes in Finance: new results for High Frequency Trading
This paper presents an overview of of the state-of-the-art in the econometric
literature on the modelling of so-called financial point processes.
Financial Point Processes comprise random arrival of specific financial
trading events, such as transactions, cancellations etc. After discussing
the strengths and weakness of most popular techniques I propose modelling
the financial point processes by a Doubly Stochastic Poisson Process
(DSPP) where the intensity process belongs to a class of affine diffusions.
For any intensity process from this class we derive an analytical expression
for probability distribution functions of the corresponding DSPP. A
specification of our results is provided in a particular case where the intensity
is given by one-dimensional Feller process and its parameters are
estimated by Kalman filtering for high frequency transaction data.