Abstract
This chapter deals with the modelling and calibration of stochastic correlations. Correlation plays essential role in pricing derivatives on multi-assets. Market observations give evidence that the correlation is hardly a deterministic quantity, however, a constant or deterministic correlation has been widely used, although it may lead to correlation risk. It has been recently proposed to model correlation by a stochastic process, similar to stochastic volatility process. In this chapter, we review the concept of stochastic correlation process including calibration via the transition density function and its application for pricing the European-style Quanto option. As an illustrating example, we compare the Quanto option prices between using constant and stochastic correlation and analyze the effect of considering stochastic correlations on pricing the Quanto option.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bowman, A.W., Azzalini, A.: Applied Smoothing Techniques for Data Analysis. Oxford University Press, New York (1997)
Brigo, D., Chourdakis, K.: Counterparty risk for credit default swaps: impact of spread volatility and default correlation. Int. J. Theor. Appl. Finance 12, 1007–1026 (2009)
Campbell, R.A.J., Forbes, C.S., Koedijk, K.G., Kofman, P.: Increasing correlations or just fat tails? J. Empir. Fin. 15, 287–309 (2008)
Carr, P., Madan, D.: Option valuation using the fast Fourier transform. J. Comput. Finance 2(4), 61–73 (1999)
Engle, R.F.: Dynamic conditional correlation: a simple class of multivariate GARCH. J. Bus. Econ. Stat. 17, 425–446 (2002)
Fang, F., Oosterlee, C.W.: A novel pricing method for European options based on Fourier-Cosine series expansions. SIAM J. Sci. Comput. 31, 826–848 (2008)
Gourieroux, C., Jasiak, J., Sufana, R.: The Wishart autoregressive process of multivariate stochastic volatility. J. Econ. 150, 167–181 (2009)
Ma, J.: Pricing foreign equity options with stochastic correlation and volatility. Ann. Econ. Finance 10, 303–327 (2009)
McNeil, A.J., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press, Princeton (2005)
Nelsen, R.: An Introduction to Copulas, 2nd edn. Springer, Berlin (2006)
Øksendal, B.: Stochastic Differential Equations. Springer, Berlin (2000)
Reiner, E.: Quanto mechanics. Risk 5(3), 59–63 (1992)
Risken, H.: The Fokker-Planck Equation. Springer, Berlin (1989)
Schöbel, R., Zhu, J.: Stochastic volatility with an Ornstein Uhlenbeck process: an extension. Eur. Finance Rev. 3, 23–46 (1999)
Teng, L., Ehrhardt, M., Günther, M.: Bilateral counterparty risk valuation of CDS contracts with simultaneous defaults. Int. J. Theor. Appl. Finance 16(7), 1350040 (2013)
Teng, L., van Emmerich, C., Ehrhardt, B., Günther, M.: A general approach for stochastic correlation using hyperbolic functions. Int. J. Comput. Math. 93(3), 524–539 (2014)
Teng, L., Ehrhardt, M., Günther, M.: Modelling stochastic correlation. J. Math. Ind. 6(1), 1–18 (2016)
Teng, L., Ehrhardt, M., Günther, M.: On the Heston model with stochastic correlation. Int. J. Theor. Appl. Finance 19(6), 1650033 (2016)
Teng, L., Ehrhardt, M., Günther, M.: Quanto pricing in stochastic correlation models. Preprint 16/15, University of Wuppertal (2016)
Uhlenbeck, G.E., Ornstein, L.S.: On the theory of Brownian motion. Phys. Rev. 36, 823–841 (1930)
van Emmerich, C.: Modelling correlation as a stochastic process. Preprint 06/03, University of Wuppertal (2006)
Wilmott, P.: Paul Wilmott on Quantitative Finance, 2nd edn. Wiley, New York (2006)
Acknowledgements
The authors were partially supported by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE—Novel Methods in Computational Finance).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Teng, L., Ehrhardt, M., Günther, M. (2017). Modelling and Calibration of Stochastic Correlation in Finance. In: Ehrhardt, M., Günther, M., ter Maten, E. (eds) Novel Methods in Computational Finance. Mathematics in Industry(), vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-61282-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-61282-9_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-61281-2
Online ISBN: 978-3-319-61282-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)