ON THE HESTON MODEL WITH STOCHASTIC CORRELATION

Long Teng, Matthias Ehrhardt () and Michael Günther ()
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Long Teng: Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany
Matthias Ehrhardt: Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany
Michael Günther: Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 06, 1-25

Abstract: The degree of relationship between financial products and financial institutions, e.g. must be considered for pricing and hedging. Usually, for financial products modeled with the specification of a system of stochastic differential equations, the relationship is represented by correlated Brownian motions (BMs). For example, the BM of the asset price and the BM of the stochastic volatility in the Heston model correlates with a deterministic constant. However, market observations clearly indicate that financial quantities are correlated in a strongly nonlinear way, correlation behaves even stochastically and unpredictably. In this work, we extend the Heston model by imposing a stochastic correlation given by the Ornstein–Uhlenbeck and the Jacobi processes. By approximating nonaffine terms, we find the characteristic function in a closed-form which can be used for pricing purposes. Our numerical results and experiment on calibration to market data validate that incorporating stochastic correlations improves the performance of the Heston model.

Keywords: Heston model; stochastic correlation process; Ornstein–Uhlenbeck process; Jacobi process; characteristic function; affine diffusion process (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (6)

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DOI: 10.1142/S0219024916500333

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