M2MO: Modélisation Aléatoire, Finance et Data Science

Master en statistique, probabilités et finance - Université Paris 7 - Paris Diderot

Courses Group Statistics and machine learning in finance Point processes and applications in finance

Point processes and applications in finance

Lecturer:  E. Löcherbach
Term 3
Schedule: 3 hours per week



(1) Introduction : Order book modeling : Market and limit orders, high frequency trading, Market endogeneity.

(2) Poisson processes (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.

(3) Order book modeling by means of self-exciting point processes. One-dimensional linear Hawkes process : denition, construction, properties, non-explosion, stationarity, law of large numbers, mean number of jumps, empirical covariation across time scales, longtime behavior.

(4) Multivariate linear Hawkes processes; Clustering representation.

(5) Statistical inference.