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Application of the heston and hull-white models to german dax data

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  • Ralf Remer
  • Reinhard Mahnke

Abstract

We focus on the stochastic description of stock price dynamics and concentrate on the Heston and Hull-White models. We derive the stationary probability density distribution of the variance of both models in the case of the zero correlation coefficient. These distributions are used to calculate solutions for the logarithmic returns of the stock price for short time lags. Furthermore, we compare the received results with numerical simulations. In addition, we apply the solutions of both models to tick-by-tick German Dax data. The data are from May 1996 to December 2001. We use the probability density distributions of the logarithmic returns calculated from the data and fit them to the theoretical distributions.

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  • Ralf Remer & Reinhard Mahnke, 2004. "Application of the heston and hull-white models to german dax data," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 685-693.
    • Handle: RePEc:taf:quantf:v:4:y:2004:i:6:p:685-693
    DOI: 10.1080/14697680500040256
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    2. Mei-Ling Cai & Zhang-HangJian Chen & Sai-Ping Li & Xiong Xiong & Wei Zhang & Ming-Yuan Yang & Fei Ren, 2022. "New volatility evolution model after extreme events," Papers 2201.03213, arXiv.org.
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    6. Buchbinder, G.L. & Chistilin, K.M., 2007. "Multiple time scales and the empirical models for stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 168-178.

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