Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Stable processes: theory and applications in finance
This thesis is a study on stable distributions and some of their applications in understanding financial markets. Three broad problems are explored: First, we study a parameter and density estimation problem for stable distributions using commodity market data. We investigate and compare the accurac...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Division of Actuarial Science
2018
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867614087271153664 |
|---|---|
| access_status_str | Open Access |
| author | Kateregga, Michael |
| author2 | Mataramvura, Sure |
| author_browse | Kateregga, Michael Mataramvura, Sure |
| author_facet | Mataramvura, Sure Kateregga, Michael |
| author_sort | Kateregga, Michael |
| collection | Thesis |
| description | This thesis is a study on stable distributions and some of their applications in understanding financial markets. Three broad problems are explored: First, we study a parameter and density estimation problem for stable distributions using commodity market data. We investigate and compare the accuracy of the quantile, logarithmic, maximum likelihood (ML) and empirical characteristic function (ECF) methods. It turns out that the ECF is the most recommendable method, challenging literature that instead suggests the ML. Secondly, we develop an affine theory for subordinated random processes and apply the results to pricing commodity futures in markets where the spot price includes jumps. The jumps are introduced by subordinating Brownian motion in the spot model by an α-stable process, α ε (0; 1] which leads to a new pricing approach for models with latent variables. The third problem is the pricing of general derivatives and risk management based on Malliavin calculus. We derive a Bismut-Elworthy-Li (BEL) representation formula for computing financial Greeks under the framework of subordinated Brownian motion by an inverse α-stable process with α ε (0; 1]. This subordination by an inverse α-stable process allows zero returns in the model rendering it fit for illiquid emerging markets. In addition, we demonstrate that the model is best suited for pricing derivatives with irregular payoff functions compared to the traditional Euler methods. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/27069 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:46:27.989Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2018 |
| publishDateRange | 2018 |
| publishDateSort | 2018 |
| publisher | Division of Actuarial Science |
| publisherStr | Division of Actuarial Science |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/27069 Stable processes: theory and applications in finance Kateregga, Michael Mataramvura, Sure Taylor, David Actuarial Science This thesis is a study on stable distributions and some of their applications in understanding financial markets. Three broad problems are explored: First, we study a parameter and density estimation problem for stable distributions using commodity market data. We investigate and compare the accuracy of the quantile, logarithmic, maximum likelihood (ML) and empirical characteristic function (ECF) methods. It turns out that the ECF is the most recommendable method, challenging literature that instead suggests the ML. Secondly, we develop an affine theory for subordinated random processes and apply the results to pricing commodity futures in markets where the spot price includes jumps. The jumps are introduced by subordinating Brownian motion in the spot model by an α-stable process, α ε (0; 1] which leads to a new pricing approach for models with latent variables. The third problem is the pricing of general derivatives and risk management based on Malliavin calculus. We derive a Bismut-Elworthy-Li (BEL) representation formula for computing financial Greeks under the framework of subordinated Brownian motion by an inverse α-stable process with α ε (0; 1]. This subordination by an inverse α-stable process allows zero returns in the model rendering it fit for illiquid emerging markets. In addition, we demonstrate that the model is best suited for pricing derivatives with irregular payoff functions compared to the traditional Euler methods. 2018-01-29T07:27:22Z 2018-01-29T07:27:22Z 2017 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/27069 eng application/pdf Division of Actuarial Science Faculty of Commerce University of Cape Town |
| spellingShingle | Actuarial Science Kateregga, Michael Stable processes: theory and applications in finance |
| thesis_degree_str | Doctoral |
| title | Stable processes: theory and applications in finance |
| title_full | Stable processes: theory and applications in finance |
| title_fullStr | Stable processes: theory and applications in finance |
| title_full_unstemmed | Stable processes: theory and applications in finance |
| title_short | Stable processes: theory and applications in finance |
| title_sort | stable processes theory and applications in finance |
| topic | Actuarial Science |
| url | http://hdl.handle.net/11427/27069 |
| work_keys_str_mv | AT katereggamichael stableprocessestheoryandapplicationsinfinance |