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

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  • Marcos Escobar
  • Barbara G�tz
  • Daniela Neykova
  • Rudi Zagst

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.

Suggested Citation

  • Marcos Escobar & Barbara G�tz & Daniela Neykova & Rudi Zagst, 2014. "Stochastic Correlation and Volatility Mean-reversion - Empirical Motivation and Derivatives Pricing via Perturbation Theory," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(6), pages 555-594, December.
    • Handle: RePEc:taf:apmtfi:v:21:y:2014:i:6:p:555-594
    DOI: 10.1080/1350486X.2014.906972
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    Cited by:

    1. M. Escobar & D. Neykova & R. Zagst, 2017. "HARA utility maximization in a Markov-switching bond–stock market," Quantitative Finance, Taylor & Francis Journals, vol. 17(11), pages 1715-1733, November.
    2. Daniela Neykova & Marcos Escobar & Rudi Zagst, 2015. "Optimal investment in multidimensional Markov-modulated affine models," Annals of Finance, Springer, vol. 11(3), pages 503-530, November.

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