Discrete-valued Lévy processes and low latency financial econometrics

Integer-valued Lévy processes and low latency financial econometrics

Motivated by features of low latency data in financial econometrics we study in detail integervalued Lévy processes as the basis of price processes for high frequency econometrics. We propose using models built out of the difference of two subordinators. We apply these models in practice to low latency data for a variety of different types of futures contracts.

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...

Lévy-driven time series models for financial data

The ARCH and GARCH models of Engle (1982) and Bollerslev (1986) respectively have had great success in the modelling of financial time series. Discrete-time stochastic volatility models have also been found to be very useful in representing the time-variation of volatility observed in such data. In this review we discuss Lévy-driven continuous-time versions of these processes and some related i...

Financial modeling with Lévy processes