Self-exciting and fractional processes in finance
(2022)
Files
PhD_Thesis_JJKetelbuters.pdf
Open Access - Adobe PDF
- 7.11 MB
Details
- Authors
- Supervisors
- Hainaut, Donatien
- Abstract
- In mathematical finance, two important purposes are to price financial products and to assess the risks that economic agents are subject to. This is done with the help of mathematical models. The 2008 financial crisis highlighted the need to take into account the risk of contagion in the mathematical models. Two areas of mathematical finance in which a risk of contagion exists are credit risk and asset price modeling. Credit risk is the risk that arises from the fact that an economic operator may not be able to meet its financial commitments, in which case we say that it defaults. When studying credit risk, the risk of contagion refers to the clustering of default events. The default of an economic agent induces financial difficulties for other economic agents, leading, through a propagation phenomenon, to clustering of defaults. When dealing with asset price modeling, the risk of contagion refers to the fact that a large sudden move in the price, also called a jump, is likely to be shortly followed by other jumps in the price of this asset, as well as in the prices of other assets. The first main topic of this thesis is the use of self-exciting processes to obtain mathematical models that take into account the risk of contagion. The second main topic of this thesis is the use of fractional processes in credit risk and asset price modeling. We show that fractional processes allow to obtain default probability curves that occur in practice but that cannot be reproduced by standard credit risk models. Finally, we show that fractional processes also allow to model illiquid assets by the introduction of motionless periods in the asset price paths.
- Affiliations
Citations
Ketelbuters, J. J. (2022). Self-exciting and fractional processes in finance. https://hdl.handle.net/2078.5/104160