This information is indicative and can be subject to change.
Financial time series analysis
Teacher: Eva Locherbach
page of the course: https://cours.univ-paris1.fr/course/view.php?id=29671
E-mail: [email protected]
ECTS: 2.5
Evaluation: Written exam.
Previsional Place and time: Thursday afternoon 13-16, starting from September 22.
Prerequisites: Basics in probability theory - but nothing more!
Aim of the course: Since the last ten years, self-exciting point processes, also called Hawkes processes, have shown to be extremely efficient to provide simple models in empirical high frequency finance. The aim of this course is to give a self-contained introduction to this class of models and to discuss how they can be used e.g. for estimating the volatility at the level of transaction data, modeling systemic risk contagion or reproducing the typical dynamic of order books.
Syllabus:
References: I will provide lecture notes.
Financial time series analysis
Teacher: Eva Locherbach
page of the course: https://cours.univ-paris1.fr/course/view.php?id=29671
E-mail: [email protected]
ECTS: 2.5
Evaluation: Written exam.
Previsional Place and time: Thursday afternoon 13-16, starting from September 22.
Prerequisites: Basics in probability theory - but nothing more!
Aim of the course: Since the last ten years, self-exciting point processes, also called Hawkes processes, have shown to be extremely efficient to provide simple models in empirical high frequency finance. The aim of this course is to give a self-contained introduction to this class of models and to discuss how they can be used e.g. for estimating the volatility at the level of transaction data, modeling systemic risk contagion or reproducing the typical dynamic of order books.
Syllabus:
- The classical Poisson process; Thinning and superposition, Law of Large Numbers and Central Limit Theorem. Poisson processes with inhomogeneous rates, Poisson random measures. Construction of processes having position dependent jump rates by time change and by Ogata's thinning algorithm.
- Limit order book modeling using self-exciting point processes. One-dimensional linear Hawkes process : definition, construction, first properties, non-explosion. Estimating the market stability.
- Construction of a stationarity version, law of large numbers, mean number of jumps, empirical covariation across time scales, cumulants, longtime behavior.
- Multivariate linear Hawkes processes; Clustering representation.
- Application to financial time series. A simple price model
- Outlook : Statistical inference and simulation.
References: I will provide lecture notes.
