Skip to main content

LUP Student Papers

LUND UNIVERSITY LIBRARIES

Dynamic Covariance Modelling Using Generalised Wishart Processes

Nilsson, Fredrik LU (2023) In Master's Theses in Mathematical Sciences FMSM01 20231
Mathematical Statistics
Abstract
Modern portfolio theory was pioneered by Markowitz who formulated the mean-variance problem, without which any discussion on quantitative approaches to portfolio selection would be incomplete. The framework boils down to finding the expected return $\mu$ and covariance $\Sigma$, after which the solution is proportional to $\Sigma^{-1}\mu$. Although the problem is simple at heart, finding estimates of the components constitutes an entire field of research. Common estimators are weighted sample means, and there exist various techniques designed to separate information from noise -- the difficulty of which makes matters even worse when inverting the covariance.

In this project, we take a more probabilistic route to modelling the... (More)
Modern portfolio theory was pioneered by Markowitz who formulated the mean-variance problem, without which any discussion on quantitative approaches to portfolio selection would be incomplete. The framework boils down to finding the expected return $\mu$ and covariance $\Sigma$, after which the solution is proportional to $\Sigma^{-1}\mu$. Although the problem is simple at heart, finding estimates of the components constitutes an entire field of research. Common estimators are weighted sample means, and there exist various techniques designed to separate information from noise -- the difficulty of which makes matters even worse when inverting the covariance.

In this project, we take a more probabilistic route to modelling the covariance and deploy a Markov chain Monte Carlo algorithm to perform Bayesian inference. We extend on existing frameworks by tailoring a Hamiltonian Monte Carlo algorithm to improve sampling efficiency. The model is validated on synthetic datasets and deployed on financial data in the form of future contract return series. Results are on par with benchmark models based on exponentially weighted moving averages, and we notice particular improvement by modelling the precision matrix $\Sigma^{-1}$ directly, thus circumventing the otherwise problematic inversion (Less)
Please use this url to cite or link to this publication:
author
Nilsson, Fredrik LU
supervisor
organization
alternative title
Dynamisk Kovariansmodellering Med Generaliserade Wishartprocesser
course
FMSM01 20231
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Covariance matrix, generalised Wishart process, Bayesian inference, Markov chain Monte Carlo, Hamiltonian Monte Carlo
publication/series
Master's Theses in Mathematical Sciences
report number
LUTFMS-3490-2023
ISSN
1404-6342
other publication id
2023:E68
language
English
id
9127026
date added to LUP
2023-08-09 09:55:25
date last changed
2023-08-23 16:14:30
@misc{9127026,
  abstract     = {{Modern portfolio theory was pioneered by Markowitz who formulated the mean-variance problem, without which any discussion on quantitative approaches to portfolio selection would be incomplete. The framework boils down to finding the expected return $\mu$ and covariance $\Sigma$, after which the solution is proportional to $\Sigma^{-1}\mu$. Although the problem is simple at heart, finding estimates of the components constitutes an entire field of research. Common estimators are weighted sample means, and there exist various techniques designed to separate information from noise -- the difficulty of which makes matters even worse when inverting the covariance. 

In this project, we take a more probabilistic route to modelling the covariance and deploy a Markov chain Monte Carlo algorithm to perform Bayesian inference. We extend on existing frameworks by tailoring a Hamiltonian Monte Carlo algorithm to improve sampling efficiency. The model is validated on synthetic datasets and deployed on financial data in the form of future contract return series. Results are on par with benchmark models based on exponentially weighted moving averages, and we notice particular improvement by modelling the precision matrix $\Sigma^{-1}$ directly, thus circumventing the otherwise problematic inversion}},
  author       = {{Nilsson, Fredrik}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Dynamic Covariance Modelling Using Generalised Wishart Processes}},
  year         = {{2023}},
}