A comparative goodness-of-fit analysis of distributions of some Lévy processes and Heston model to stock index returns

Ahmet Goncu, Mehmet Karahan and Tolga Kuzubas

The North American Journal of Economics and Finance, 2016, vol. 36, issue C, 69-83

Abstract: In this paper, we investigate the goodness-of-fit of three Lévy processes, namely Variance-Gamma (VG), Normal-Inverse Gaussian (NIG) and Generalized Hyperbolic (GH) distributions, and probability distribution of the Heston model to index returns of twenty developed and emerging stock markets. Furthermore, we extend our analysis by applying a Markov regime switching model to identify normal and turbulent periods. Our findings indicate that the probability distribution of the Heston model performs well for emerging markets under full sample estimation and retains goodness of fit for high volatility periods, as it explicitly accounts for the volatility process. On the other hand, the distributions of the Lévy processes, especially the VG and NIG distributions, generally improves upon the fit of the Heston model, particularly for developed markets and low volatility periods. Furthermore, some distributions yield to significantly large test statistics for some countries, even though they fit well to other markets, which suggest that properties of the stock markets are crucial in identifying the best distribution representing empirical returns.

Keywords: Variance-gamma model; Normal-inverse gaussian model; Generalized hyperbolic model; Heston model; Markov regime-switching model; Emerging markets (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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Related works:
Working Paper: A Comparative Goodness-of-fit Analysis of Distributions of Some Levy Processes and Heston Model to Stock Index Returns (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecofin:v:36:y:2016:i:c:p:69-83

DOI: 10.1016/j.najef.2015.12.001

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