Computational Management Science

, Volume 15, Issue 2, pp 239–258

# Modeling and implementation of local volatility surfaces in Bayesian framework

• Abdulwahab Animoku
• Ömür Uğur
• Yeliz Yolcu-Okur
Original Paper

## Abstract

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.

## Keywords

Local volatility model Bayesian analysis Tikhonov regularization

## Notes

### Acknowledgements

The author, Abdulwahab Animoku, acknowledges The Scientific and Technological Research Council of Turkey (TÜBİTAK) for its financial support throughout his graduate studies.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

## Authors and Affiliations

• Abdulwahab Animoku
• 1
• Ömür Uğur
• 1
• Yeliz Yolcu-Okur
• 1
1. 1.Institute of Applied MathematicsMiddle East Technical UniversityÇankayaTurkey