Abstract
It is well known that the correlation between financial products, financial institutions, e.g., plays an essential role in pricing and evaluation of derivatives. Using a constant or deterministic correlation may lead to correlation risk, since market observations give evidence that the correlation is hardly a deterministic quantity.
Here, the approach of Teng et al. (A versatile approach for stochastic correlation using hyperbolic functions. Preprint 13/14. University of Wuppertal, 2013) for modelling the correlation as a hyperbolic function of a stochastic process is generalized to derive stochastic correlation processes (SCP) from a hyperbolic transformation of the modified Ornstein-Uhlenbeck process. We determine a transition density function of this SCP in closed form which could be used easily to calibrate SCP models to historical data.
As an example we compute the price of a quantity adjusting option (Quanto) and discuss concisely the effect of considering stochastic correlation on pricing the Quanto.
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Acknowledgements
The authors were partially supported by the European Union in the FP7-PEOPLE-2012-ITN Programme under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE—Novel Methods in Computational Finance).
The authors acknowledge partial support from the bilateral German-Spanish Project HiPeCa—High Performance Calibration and Computation in Finance, Programme Acciones Conjuntas Hispano-Alemanas financed by DAAD.
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Teng, L., Ehrhardt, M., Günther, M. (2016). Modelling Stochastic Correlation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds) Progress in Industrial Mathematics at ECMI 2014. ECMI 2014. Mathematics in Industry(), vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-23413-7_14
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DOI: https://doi.org/10.1007/978-3-319-23413-7_14
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