A versatile approach for stochastic correlation using hyperbolic functions

L Teng, C Van Emmerich, M Ehrhardt… - International Journal of …, 2016 - Taylor & Francis
L Teng, C Van Emmerich, M Ehrhardt, M Günther
International Journal of Computer Mathematics, 2016Taylor & Francis
It is well known that the correlation between financial products or financial institutions, eg
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 …
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.
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