Uncertainty quantification of parameters in local volatility model via frequentist, Bayesian and stochastic Galerkin methods

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Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Uygulamalı Matematik Enstitüsü, Bilimsel Hesaplama Anabilim Dalı, Türkiye

Tezin Onay Tarihi: 2018

Öğrenci: ABDULWAHAB ADINOYI ANIMOKU

Danışman: ÖMÜR UĞUR

Özet:

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.