Bergische Universität Wuppertal Fachbereich Mathematik und Naturwissenschaften Angewandte Mathematik - Numerische Analysis

People Research Publications Teaching

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Modelling Stochastic Correlations in Finance

Masterarbeit Mathematik

Supervision

• Prof. Dr. Matthias Ehrhardt
• Prof. Dr. Michael Günther

Description

In this thesis we will revisit the ideas of Cathrin van Emmerich and Jun Ma and propose some modifications and generalizations.

Keywords

Stochastic correlation, correlation risk, hyperbolic functions, stochastic process, Ornstein- Uhlenbeck process, Quanto, Fokker-Planck equation, WASC model.

References:

1. A. Alvarez, M. Escobar, P. Olivares, Pricing two dimensional derivatives under stochastic correlation, Int. J. Financial Markets Deriv. 2 (2011), 265-287.
2. X. Burtschell, J. Gregory and J-P. Laurent, Beyond the Gaussian copula: Stochastic and Local Correlation, Journal of Credit Risk 3 (2007), 31-62.
3. A. Buraschi, A. Cieslak, F. Trojani, Correlation risk and the term structures of interest rates, Working paper, Imperial College, London, 2007.
4. A. Buraschi, P. Porchia, F. Trojani, Correlation risk and optimal portfolio choice, The Journal of Finance 65 (2010), 393-420.
5. P. Collin-Dufresne, R. Goldstein, Stochastic Correlation and the Relative Pricing of Caps and Swaptions in a Generalized-Affine Framework, EFA 2002 Berlin Meetings Presented Paper. 2001.
6. J. Driessen, P. Maenhout, G. Vilkov, Option-Implied correlations and the price of correlation risk, working paper, INSEAD, 2006.
7. M. Escobar, B. Götz, L. Seco, R. Zagst, Pricing of spread options on stochastically correlated underlyings, J. Comput. Fin. 12 (2009), 31-61.
8. J. Fonseca, M. Grasselli, C. Tebaldi, Option pricing when correlations are stochastic: An analytical framework, Review of Derivatives Research 10 (2007), 151-180.
9. J. Fonseca, M. Grasselli, F. Ielpo, Estimating the Wishart Affine Stochastic Correlation Model Using the Empirical Characteristic Function, (August 13, 2012). Available at SSRN: http://ssrn.com/abstract=1054721 or http://dx.doi.org/10.2139/ssrn.1054721
10. B.M. Götz, Valuation of multi-dimensional derivatives in a stochastic covariance framework, Dissertation, TU München, 2011.
11. A. Hamidreza, Financial Engineering of the Stochastic Correlation in Credit Risk Models, Dissertation, University of Toronto, 2010.
12. J. Ma, A Stochastic Correlation Model with Mean Reversion for Pricing Multi-Asset Options, Asia-Pacific Financial Markets 16 (2009), 97-109.
13. J. Ma, Pricing Foreign Equity with Stochastic Correlation and Volatility, Annals of Finance and Economics 10 (2009), 303-327.
14. J. Ma, Multi-factor models for pricing correlation-dependent interest-rate contingent claim, International Review of Applied Financial Issues and Economics 2 (2010), 359-378
15. J. Marabel Romo, Worst-Of Options and Correlation Skew Under a Stochastic Correlation Framework, Int. J. Theoret. Appl. Fin.15 (2012), 32 pages.
16. S. Sepp, Modeling of stock return correlation, University of Amsterdam, Master Thesis, 2011.
17. L. Teng, C. van Emmerich, M. Ehrhardt and M. Günther, A General Approach for Stochastic Correlation using Hyperbolic Functions, Preprint 13/14, August 2013.
18. C. van Emmerich, Modelling Correlation as a Stochastic Process, Preprint 06/03, University of Wuppertal, June 2006.
19. C. van Emmerich, Stochastic Mean Reversion in the Large Homogeneous Portfolio Model, Preprint 07/02, University of Wuppertal, May 2007.
20. C. van Emmerich, A Square Root Process for Modelling Correlation, University of Wuppertal, Dissertation, 2007.