Master's Thesis

This repository contains the code used for the creation of my Master's Thesis in Mathematics-Economics. Investigation of the Burst Hypothesis and Intraday Volatility Behaviour

Abstract

This thesis expands the theory and mathematical foundation behind the ex- istence of short-lived explosive trends in the financial markets, split into the explosion of the volatility and explosion of drift as first described in Chris- tensen et al. (2016). We add finite sample corrections and extra parame- ter tuning to the estimators, allowing us to improve the detection of periods with extremely high volatility and possibly drift. With fast computational algorithms, we create thorough simulation studies showing that these periods cannot be described by the standard Heston model with a jump component. However, we also provide evidence that conclusions drawn from the Heston model does not necessarily extend to financial markets, particularly S&P 500. To remedy this, a thorough study of volatility is conducted. The empirical behaviour of volatility is investigated and volatility is modelled utilizing Brow- nian semi-stationary processes as introduced in Barndorff-Nielsen & Schmiegel (2009) in an attempt to capture both roughness and persistence along with intraday seasonality.
Ultimately, the simulation study is extended to a model featuring a Brownian semi-stationary process, which strengthens the hypothesis of the existence of the short-lived explosive periods as even such models fall short of explaining these extreme events, denoted as bursts. This allows us to show the presence of bursts on S&P 500 but question whether drift bursts are present or the bursts are in fact all explained by an explosion in the volatility. We also apply the theory on Bitcoin and justify the existence of both volatility bursts and drift bursts in this market, though high-frequency frictions on the exchanges make these conclusions uncertain.

Authors

Sebastian G. Pedersen (sebastian.g.pedersen@gmail.com)
Frederik Skjøtt
Mathias Wilken

If this is of interest, please don't hesitate to reach out.