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A Parsimonious Multi-Asset Heston Model: Calibration And Derivative Pricing

Author

Listed:
  • GEORGI DIMITROFF

    (DZ Bank AG, Platz der Republik, 60265 Frankfurt am Main, Germany)

  • STEFAN LORENZ

    (Fraunhofer ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany)

  • ALEXANDER SZIMAYER

    (Department of Business Administration, University of Hamburg, Von-Melle-Park 5, 20146 Hamburg, Germany)

Abstract

We propose a parsimonious multi-asset Heston model and provide an easy-to-implement calibration algorithm. The model is customized to pricing multi-asset options in markets with liquidly traded single-asset options but no liquidly traded cross-asset options. In this situation, single-asset model parameters can be calibrated from option price data, however, cross-asset parameters cannot. We formulate a parsimonious model specification such that all single-asset models are Heston models, which are affine allowing for efficient calibration of the respective parameters. The single-asset models are correlated using cross-asset correlations only. Cross-asset correlations are observable, in contrast to correlations of latent variables such as volatilities, and serve as basis for calibration. A hybrid calibration approach for identifying the model parameters consistent with option price data and asset price data is outlined and illustrated by a case study. In banking practice the approach is referred to as correlation adjustment.

Suggested Citation

  • Georgi Dimitroff & Stefan Lorenz & Alexander Szimayer, 2011. "A Parsimonious Multi-Asset Heston Model: Calibration And Derivative Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(08), pages 1299-1333.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:08:n:s021902491100653x
    DOI: 10.1142/S021902491100653X
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    Cited by:

    1. Baron Law, 2021. "Correlation Estimation in Hybrid Systems," Papers 2111.06042, arXiv.org, revised Jul 2023.
    2. Howard Caulfield & James P. Gleeson, 2024. "Systematic comparison of deep generative models applied to multivariate financial time series," Papers 2412.06417, arXiv.org.

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