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Articles

A versatile approach for stochastic correlation using hyperbolic functions

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Pages 524-539 | Received 06 Aug 2013, Accepted 22 Dec 2014, Published online: 29 Jan 2015
 

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.

2010 AMS Subject Classifications:

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.

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