Modelling of Financial Bubbles: The LPPLS model: Theoretical presentation and test

Martin Hoshi Vognsen

Student thesis: Master thesis


This thesis presents the LPPLS-model for identification of financial bubbles. The objective of the model is to estimate the most probable time of a crash. A bubble is defined by a log-periodic power law (LPPL) process and estimation of the most probable time of a crash relies on the existence of a critical time defined by an LPPL singularity. The thesis lays the theoretical foundation for implementing and calibrating the model as well as interpreting its output. Parametrization and inference is discussed with a focus on the parametrization proposed by Filimonov and Sornette in 2013. Diagnostics of the model and its results are discussed through simulation-based examples. Finally I demonstrate application of the model on a time series of the S&P 500 Composite Index in a period leading up to the 2020 crash.

EducationsMSc in Business Administration and Mathematical Business Economics, (Graduate Programme) Final Thesis
Publication date2021
Number of pages83
SupervisorsPeter Dalgaard