Azencott, Robert2019-05-23August 2012018-08August 201https://hdl.handle.net/10657/4003Stochastic volatility models, in finance, study the volatility dynamics of the asset pricing process. It is the assumption of the randomness of the volatility of a underlying asset not directly observable, that allows for these models to improve the accuracy of computation of the pricing process and its forecasts. Stochastic Differential equations (SDEs) model such randomness in volatility along with the pricing process. Heston model is a widely used stochastic volatility model that goverened by five unknown parameters. Estimation of these parameters help us obtain an evolution for assest price and its corresponding volatility process that is consistent with real time option prices. In this thesis, we investigate the behaviour of the Maximum likelihood estimates for the parameters of the Heston model in a non-Gaussian regime. In particular, we study the MLEs when the ratio of the parameters of the volatility equation of the Heston model, satisfying the classical Feller condition, falls under a certain critical value. We demonstrate that the asymptotic behavior of parameters can be described as rational functions which involve variables following the stable distribution. We also develop a strategy to estimate parameters of the stable distribution and verify our approach using numerical simulations.application/pdfengThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).Stochastic volatilityStochastic differential equations (SDE)Heston modelParameter estimationMLEStable distribution2019-05-23Thesisborn digital