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Title: Time-change and control of stochastic volatility
Author: Monge, Adriana Ocejo
ISNI:       0000 0004 5361 126X
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2014
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics