Uncertainty quantification of parameters in local volatility model via frequentist, bayesian and stochastic galerkin methods

Animoku, Abdulwahab
In this thesis, we investigate and implement advanced methods to quantify uncertain parameter(s) in Dupire local volatility equation. The advanced methods investigated are Bayesian and stochastic Galerkin methods. These advanced techniques implore different ideas in estimating the unknown parameters in PDEs. The Bayesian approach assumes the parameter is a random variable to be sampled from its posterior distribution. The posterior distribution of the parameter is constructed via “Bayes theorem of inverse problem”. Stochastic Galerkin method involves propagating uncertainty into a deterministic input parameter and then quantifying the randomness in the solution. In addition, the performance and numerical analysis of each approach are studied.


Stochastic modelling of biochemical networks and inference of modelparameters
Purutçuoğlu Gazi, Vilda (null, Springer, 2018-01-01)
There are many approaches to model the biochemical systems deterministically or stochastically. In deterministic approaches, we aim to describe the steady-state behaviours of the system, whereas, under stochastic models, we present the random nature of the system, for instance, during transcription or translation processes. Here, we represent the stochastic modelling approaches of biological networks and explain in details the inference of the model parameters within the Bayesian framework.
Inference in multivariate linear regression models with elliptically distributed errors
İslam, Muhammed Qamarul; Yazici, Mehmet (2014-08-01)
In this study we investigate the problem of estimation and testing of hypotheses in multivariate linear regression models when the errors involved are assumed to be non-normally distributed. We consider the class of heavy-tailed distributions for this purpose. Although our method is applicable for any distribution in this class, we take the multivariate t-distribution for illustration. This distribution has applications in many fields of applied research such as Economics, Business, and Finance. For estimat...
Modeling and implementation of local volatility surfaces in Bayesian framework
Animoku, Abdulwahab; Uğur, Ömür; Yolcu-Okur, Yeliz (2018-06-01)
In this study, we focus on the reconstruction of volatility surfaces via a Bayesian framework. Apart from classical methods, such as, parametric and non-parametric models, we study the Bayesian analysis of the (stochastically) parametrized volatility structure in Dupire local volatility model. We systematically develop and implement novel mathematical tools for handling the classical methods of constructing local volatility surfaces. The most critical limitation of the classical methods is obtaining negativ...
Multi-objective decision making using fuzzy discrete event systems: A mobile robot example
Boutalis, Yiannis; Schmidt, Klaus Verner (2010-09-29)
In this paper, we propose an approach for the multi-objective control of sampled data systems that can be modeled as fuzzy discrete event systems (FDES). In our work, the choice of a fuzzy system representation is justified by the assumption of a controller realization that depends on various potentially imprecise sensor measurements. Our approach consists of three basic steps that are performed in each sampling instant. First, the current fuzzy state of the system is determined by a sensor evaluation. Seco...
Estimation and hypothesis testing in multivariate linear regression models under non normality
İslam, Muhammed Qamarul (Informa UK Limited, 2017-01-01)
This paper discusses the problem of statistical inference in multivariate linear regression models when the errors involved are non normally distributed. We consider multivariate t-distribution, a fat-tailed distribution, for the errors as alternative to normal distribution. Such non normality is commonly observed in working with many data sets, e.g., financial data that are usually having excess kurtosis. This distribution has a number of applications in many other areas of research as well. We use modifie...
Citation Formats
A. Animoku, “Uncertainty quantification of parameters in local volatility model via frequentist, bayesian and stochastic galerkin methods,” Ph.D. - Doctoral Program, Middle East Technical University, 2018.