Modelling Fat Tails Using Alternative Leptokurtic Distributions : A Case Study of India’s Nifty50 Index
Financial returns modelling assumes that price returns are normally distributed, which is problematic because it fails to capture “fat tails”, or extreme price swings, that are commonly observed in the financial markets. This has led to increased interest in alternative distribution models that may be better able to capture fat tails. In this study, we aimed to determine whether leptokurtic distributions, which are non-normal and characterised by a higher degree of kurtosis, are more effective at predicting extreme price movements than normal distributions.Using India's Nifty50 Index as the sample, we conducted several Goodness of Fit tests to assess normality. Our results showed a consistently high empirical kurtosis value, rejecting the normality hypothesis. We then explored the suitability of leptokurtic distributions for modelling extreme movements, calibrating the distributions with Maximum Likelihood Estimation and the log- likelihood function. We also utilised ‘the rolling-window analysis of time series for parameter stability’ to account for temporal changes. Based on the overall performance of the distributions, we utilised MLE and Akaike Information Criteria to conclude that the generalised Student's t- distribution was the most suitable model for our sample data. Importantly, we also investigated the critical issue of assigning probabilities to fat-tailed risks and found evidence that the generalised Student's t-distribution model is much more reliable at estimating extreme price movements than a Gaussian distribution model. As per the proposed model, extreme price swings seem to be a regular feature of the market rather than an anomaly and should therefore not be regarded as outliers.To our knowledge, this is the first study to conduct a comparison of leptokurtic distributions with the explicit aim of applying the most appropriate model to the largest exchange in the world, namely the Nifty50 Index. However, our study is also limited by the fact that it examines only one exchange, so broader conclusions cannot be drawn. It is also essential to bear in mind that the Student's t-distribution is not a “true model” and should not be applied to other datasets without prior verification. Our discussion emphasises the necessity of carefully and thoroughly evaluating any statistical model before using it, consistent with the widely held principle that “all models are wrong, but some are useful”. The purpose of this study was not to propose a replacement for the normal distribution model. Our goal was to enhance our understanding of alternative models that may address current deficiencies in financial analysis. As Keynes proclaimed, “it is better to be roughly right than precisely wrong”
Year of publication: |
2022
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Authors: | Khan, Saud Amin |
Publisher: |
[S.l.] : SSRN |
Subject: | Indien | India | Statistische Verteilung | Statistical distribution | Schätztheorie | Estimation theory | Wahrscheinlichkeitsrechnung | Probability theory |
Saved in:
freely available
Extent: | 1 Online-Ressource (56 p) |
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Type of publication: | Book / Working Paper |
Language: | English |
Notes: | Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments July 01, 2022 erstellt |
Other identifiers: | 10.2139/ssrn.4308221 [DOI] |
Classification: | c58 ; G1 - General Financial Markets |
Source: | ECONIS - Online Catalogue of the ZBW |
Persistent link: https://www.econbiz.de/10014255212
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