Abstract
Association or interdependence of two stock prices is analyzed, and selection criteria for a suitable model developed in the present paper. The association is generated by stochastic correlation, given by a stochastic differential equation (SDE), creating interdependent Wiener processes. These, in turn, drive the SDEs in the Heston model for stock prices. To choose from possible stochastic correlation models, two goodness-of-fit procedures are proposed based on the copula of Wiener increments. One uses the confidence domain for the centered Kendall function, and the other relies on strong and weak tail dependence. The constant correlation model and two different stochastic correlation models, given by Jacobi and hyperbolic tangent transformation of Ornstein-Uhlenbeck (HtanOU) processes, are compared by analyzing daily close prices for Apple and Microsoft stocks. The constant correlation, i.e., the Gaussian copula model, is unanimously rejected by the methods, but all other two are acceptable at a 95% confidence level. The analysis also reveals that even for Wiener processes, stochastic correlation can create tail dependence, unlike constant correlation, which results in multivariate normal distributions and hence zero tail dependence. Hence models with stochastic correlation are suitable to describe more dangerous situations in terms of correlation risk.
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15 May 2021
A Correction to this paper has been published: https://doi.org/10.1007/s11009-021-09868-4
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Acknowledgements
We acknowledge with sincere appreciation and gratitude that the computer program for estimating the Heston model parameters by the MCMC algorithm was given to us by one of the authors of Cape et al. (2015), Qin Lu. Even though we modified the program in order to gain computational speed and changed the update distribution of the variance process, it has proven to be a tremendous help to have the original version and start our work with it. Therefore we feel greatly indebted to them. The first author gratefully acknowledges partial support by the Fulbright Teaching and Research Award while finishing this research and writing part of the present paper in the Department of Statistics, University of Connecticut.
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Márkus, L., Kumar, A. Modelling Joint Behaviour of Asset Prices Using Stochastic Correlation. Methodol Comput Appl Probab 23, 341–354 (2021). https://doi.org/10.1007/s11009-020-09838-2
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DOI: https://doi.org/10.1007/s11009-020-09838-2
Keywords
- Correlation risk
- Heston model
- Kendall function
- Stochastic correlation
- Stock price association
- Tail dependence