Learning objectives

The course aims to introduce the class of semimartingale processes with jumps, used in the literature as financial asset price models, and to provide tools for estimating and testing jumps in financial asset prices

Prerequisites and basic notions

Basic probability, basic statistics, Brownian motion, Ito integral

Program

Poisson process, random measures and Poisson random measures
Semimartingales with jumps and Lévy processes
Semimartingale models for financial asset prices: Brownian SM, finite activity jumps, infinite activity jumps, pure jump models
Quadratic variation
Estimating the jumps given discrete observations
Testing for jumps

Bibliography

Didactic methods

Classroom lessons, assignments consisting of the study of the proof of some results to be told and commented on in class

Learning assessment procedures

Each student can choose either a written exam about one of the topics dealt with during the course, or an individual written and reasoned report deepening one of the topics proposed after the course

Assessment

Rigor, creativity, exposure

Criteria for the composition of the final grade

Rigor 4 points out of 10, creativity 3, exposure 3

Scheduled Lessons