Integer-valued Lévy processes and low latency financial econometrics

Discrete-valued Lévy processes and low latency financial econometrics

Motivated by features of low latency data in finance we study in detail discrete-valued Lévy processes as the basis of price processes for high frequency econometrics. An important case of this is a Skellam process, which is the difference of two independent Poisson processes. We propose a natural generalisation which is the difference of two negative binomial processes. We apply these models i...

Modelling by Lévy Processes for Financial Econometrics

This paper reviews some recent work in which Lévy processes are used to model and analyse time series from financial econometrics. A main feature of the paper is the use of positive OrnsteinUhlenbeck (OU) type processes inside stochastic volatility processes. The basic probability theory associated with such models is discussed in some detail.

Conditional distributions of Mandelbrot-Van Ness fractional Lévy processes and continuous-time ARMA-GARCH-type models with long memory

Long memory effects can be found in different kind of data from finance to hydrology. Therefore, models which can reflect these properties have become more popular in recent years especially in the fields of time series analysis, econometrics and financial mathematics. Mandelbrot-Van Ness fractional Lévy processes allow for such stationary long memory effects in their increments and have been u...

Integer-valued trawl processes: A class of stationary infinitely divisible processes

This paper introduces a new continuous-time framework for modelling serially correlated count and integer-valued data. The key component in our new model is the class of integer-valued trawl (IVT) processes, which are serially correlated, stationary, infinitely divisible processes. We analyse the probabilistic properties of such processes in detail and, in addition, study volatility modulation ...

Financial modeling with Lévy processes