Dynamic Covariance Modelling Using Generalised Wishart Processes
(2023) In Master's Theses in Mathematical Sciences FMSM01 20231Mathematical 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:
http://lup.lub.lu.se/student-papers/record/9127026
- author
- Nilsson, Fredrik LU
- supervisor
- organization
- alternative title
- Dynamisk Kovariansmodellering Med Generaliserade Wishartprocesser
- course
- FMSM01 20231
- year
- 2023
- 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}}, }