PhD Project: Alternative stochastic models in Finance
The celebrated Black-Scholes formula has been derived under the assumption of constant volatility in stocks. In spite of evidence that this parameter is not constant, this formula is widely used by the markets. It is therefore natural to ask whether a model for stock price exists such that the Black-Scholes formula holds while the volatility is non-constant. This project attempts to answer the more general question of the existence of alternative models, in the theory of stochastic processes and its applications and in particular finance. It will continue similar work on the construction of certain processes (in particular self-similar Markov martingales) with given marginals by Fan, Hamza and Klebaner.
[1] Fan, Jie Yen, Kais Hamza, and Fima Klebaner. “Mimicking self-similar processes.” Bernoulli 21.3 (2015): 1341-1360.
[2] Hamza, Kais, and Fima C. Klebaner. “A Family of Non-Gaussian Martingales with Gaussian Marginals-Volume 2007, Article ID 92723, 19 pages.” JAMSA-Journal of Applied Mathematics and Stochastic Analysis 1 (2007).
Applications can be made by selecting the below link.
Please attach supporting documentation including a covering letter outlining why you would like to undertake the PhD project and a current CV including 2 referees. Please note that more than one application can be made if you wish to be considered for more than one PhD project.