Stability of deterministic signals in stochastic financial stock price data
Date
2026
Authors
Hilder, Charles
Journal Title
Journal ISSN
Volume Title
Publisher
University of Victoria
Abstract
The focus of this project is to quantify the persistence of deterministic trends within stock price paths from the S&P500. We start by considering "synthetic assets" – linear combinations of held and shorted stocks, which are designed based on underlying financial theory to exhibit predictable behaviour. We then model the synthetic assets out of sample by mapping their price paths to a non euclidean space, where their evolution can be described approximately linearly using a best fit Koopman operator (K). Then using this linear approximation, we asses the persistence of the fitted operator K by the use of spectral analysis and a stochastic adaptation of Lyapunov stability theory.
Description
Keywords
math, statistics, finance, modelling, dynamic-systems, Jamie Cassels Undergraduate Research Awards (JCURA)