Stochastic Correlation and Volatility Mean-reversion - Empirical Motivation and Derivatives Pricing via Perturbation Theory

Marcos Escobar Anel (), Barbara G�tz, Daniela Neykova and Rudi Zagst

Applied Mathematical Finance, 2014, vol. 21, issue 6, 555-594

Abstract: The dependence structure is crucial when modelling several assets simultaneously. We show for a real-data example that the correlation structure between assets is not constant over time but rather changes stochastically, and we propose a multidimensional asset model which fits the patterns found in the empirical data. The model is applied to price multi-asset derivatives by means of perturbation theory. It turns out that the leading term of the approximation corresponds to the Black-Scholes derivative price with correction terms adjusting for stochastic volatility and stochastic correlation effects. The practicability of the presented method is illustrated by some numerical implementations. Furthermore, we propose a calibration methodology for the considered model.

Date: 2014
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DOI: 10.1080/1350486X.2014.906972

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