The Library
Time-change and control of stochastic volatility
Tools
Monge, Adriana Ocejo (2014) Time-change and control of stochastic volatility. PhD thesis, University of Warwick.
|
PDF
WRAP_THESIS_Monge_2014.pdf - Submitted Version - Requires a PDF viewer. Download (701Kb) | Preview |
|
Other (Permission e-mail)
FW Digitisation of your PhD thesis.msg Embargoed item. Restricted access to Repository staff only Download (68Kb) |
Official URL: http://webcat.warwick.ac.uk/record=b2730158~S1
Abstract
The central theme of this thesis is the behavior of the value function of general optimal stopping problems under a stochastic volatility model when varying the volatility dynamics. We first use a combination of time-change and coupling techniques to show regularity properties of the value function. We consider a large class of terminal payoffs: when the first component of the model is a stochastic differential equation without drift we allow for general measurable functions, and when it has a drift we impose a mild condition which includes possibly unbounded and discontinuous functions. We also consider a running cost which can be any non-negative and bounded Borel function. Moreover, we derive the solution of a zero-sum game of stopping and control, which arises when considering some parameter uncertainty in the volatility dynamics. In both finite and infinite horizon, we exhibit the existence of a saddle point using stochastic control and martingale arguments as well as the probabilistic representation of solutions to free-boundary problems.
Overall, our approach in mainly theoretical, however we impose only verifiable conditions. We then discuss some examples arising in American option pricing where our results are applicable. In particular, we are able to compare American option prices under different volatility models in a variety of settings and we establish that the optimal exercise boundary for the associated option is a monotone function of the volatility.
Item Type: | Thesis (PhD) | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Optimal stopping (Mathematical statistics), Stochastic processes | ||||
Official Date: | April 2014 | ||||
Dates: |
|
||||
Institution: | University of Warwick | ||||
Theses Department: | Department of Statistics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Assing, Sigurd ; Jacka, Saul D. | ||||
Extent: | v, 119 leaves | ||||
Language: | eng |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |