Modeling and implementation of local volatility surfaces in Bayesian framework

Animoku, Abdulwahab
Uğur, Ömür
Yolcu-Okur, Yeliz
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 negative local variances due to the ill-posedness of the numerator and/or denominator in Dupire local variance equation. While several numerical techniques, such as Tikhonov regularization and spline interpolations have been suggested to tackle this problem, we follow a more direct and robust approach. With the Bayesian analysis, choosing a suitable prior on the positive plane eliminates the undesired negative local variances.


Bayesian modelling for asymmetric multi-modal circular data
Kılıç, Muhammet Burak; Kalaylıoğlu Akyıldız, Zeynep Işıl; Sengupta, Ashis; Department of Statistics (2015)
In this thesis, we propose a Bayesian methodology based on sampling importance re-sampling for asymmetric and bimodal circular data analysis. We adopt Dirichlet process (DP) mixture model approach to analyse multi-modal circular data where the number of components is not known. For the analysis of temporal circular data, such as hourly measured wind directions, we join DP mixture model approach with circular times series modelling. The approaches are illustrated with both simulated and real life data sets. ...
Elfarra, Monier A.; Akmandor, I. Sinan; Sezer Uzol, Nilay (2011-03-25)
The main purpose of this paper is to optimize winglet geometry by using CFD with Genetic Algorithm and study its effects on power production. For validation and as a baseline rotor, the NREL Phase VI wind turbine rotor blade is used. The Reynolds-Averaged Navier-Stokes equations are solved and different turbulence models including the Spalart-Allmaras, k-epsilon Launder-Sharma, k-epsilon Yang-Shih and SST k-omega models are used and tested. The results of the power curve and the pressure distribution at dif...
Batmaz, İnci; Kartal-Koc, Elcin; Köksal, Gülser (2010-02-04)
Multivariate Adaptive Regression Splines (MARS) is a very popular nonparametric regression method particularly useful for modeling nonlinear relationships that may exist among the variables. Recently, we developed CMARS method as an alternative to backward stepwise part of the MARS algorithm. Comparative studies have indicated that CMARS performs better than MARS for modeling nonlinear relationships. In those studies, however, only main and two-factor interaction effects were sufficient to model the nonline...
Probabilistic Slope Stability Analyses Using Limit Equilibrium and Finite Element Methods
Akbas, Burak; Huvaj Sarıhan, Nejan (2015-10-16)
This paper compares the results of different probabilistic approaches and emphasizes the necessity of probabilistic analyses in slope stability studies. To do that, Limit Equilibrium Method (LEM) and Finite Element Method (FEM) are utilized and their outputs are compared in terms of probability of failure (PF), reliability index (RI), factor of safety (FS) and the failure surface. Lastly, concept of Random Finite Element Method (RFEM) is studied and effects of spatial correlation distance are investigated.
Hybrid wavelet-neural network models for time series data
Kılıç, Deniz Kenan; Uğur, Ömür; Department of Financial Mathematics (2021-3-3)
The thesis aims to combine wavelet theory with nonlinear models, particularly neural networks, to find an appropriate time series model structure. Data like financial time series are nonstationary, noisy, and chaotic. Therefore using wavelet analysis helps better modeling in the sense of both frequency and time. S&P500 (∧GSPC) and NASDAQ (∧ IXIC) data are divided into several components by using multiresolution analysis (MRA). Subsequently, each part is modeled by using a suitable neural network structure. ...
Citation Formats
A. Animoku, Ö. Uğur, and Y. Yolcu-Okur, “Modeling and implementation of local volatility surfaces in Bayesian framework,” COMPUTATIONAL MANAGEMENT SCIENCE, pp. 239–258, 2018, Accessed: 00, 2020. [Online]. Available: