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Abstract
It is well known that the correlation between financial products or financial institutions, e.g. plays an essential role in pricing and evaluation of financial derivatives. Using simply a constant or deterministic correlation may lead to correlation risk, since market observations give evidence that correlation is not a deterministic quantity. In this work, we propose a new approach to model the correlation as a hyperbolic function of a stochastic process. Our general approach provides a stochastic correlation which is much more realistic to model real- world phenomena and could be used in many financial application fields. Furthermore, it is very flexible: any mean-reverting process (with positive and negative values) can be regarded and no additional parameter restrictions appear which simplifies the calibration procedure. As an example, we compute the price of a Quanto applying our new approach. Using our numerical results we discuss concisely the effect of considering stochastic correlation on pricing the Quanto.
Acknowledgements
We are very grateful to the anonymous referee and the associate editor for a number of valuable comments and suggestions that has lead to a significantly improved manuscript.
The work of the first, third and fourth author was 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). Further 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.
Disclosure statement
No potential conflict of interest was reported by the authors.