A note on “Modelling exchange rate returns: which flexible distribution to use?”

Nadarajah, Saralees; Afuecheta, Emmanuel; Chan, Stephen

doi:10.1080/14697688.2015.1032997

Cited by 15 publications

(13 citation statements)

References 21 publications

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“…Here, we mention seven of the most recent papers: Corlu and Corlu (2015) compare the performance of the generalized lambda distribution against other flexible distributions such as the skewed t distribution, unbounded Johnson family of distributions, and the normal inverse Gaussian distribution, in capturing the skewness and peakedness of the returns of exchange rates. They conclude that for the Value-at-Risk and Expected Shortfall, the generalised lambda distribution gives a similar performance, and in general it can be used as an alternative for fitting the heavy tail behaviour in financial data; Nadarajah et al (2015) revisit the study of exchange rate returns in Corlu and Corlu (2015), and show that the Student's t distribution can give a similar performance to those of the distributions tested in Corlu and Corlu (2015); Bruneau and Moran (2017) investigate the effect of exchange rate fluctuations on labour market adjustments in Canadian manufacturing industries; Dai et al (2017) examine the role of exchange rates on economic growth in east Asian countries; Parlapiano et al (2017) examine exchange rate risk exposure on the value of European firms; Schroeder (2017) investigates the macroeconomic performance in developing countries with respect to exchange rates; Seyyedi (2017) provides an analysis of the interactive linkages between gold prices, oil prices, and the exchange rate in India.…”

Section: Introductionmentioning

confidence: 99%

A Statistical Analysis of Cryptocurrencies

Chan¹,

Chu²,

Nadarajah³

et al. 2017

JRFM

Self Cite

142

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Abstract:We analyze statistical properties of the largest cryptocurrencies (determined by market capitalization), of which Bitcoin is the most prominent example. We characterize their exchange rates versus the U.S. Dollar by fitting parametric distributions to them. It is shown that returns are clearly non-normal, however, no single distribution fits well jointly to all the cryptocurrencies analysed. We find that for the most popular currencies, such as Bitcoin and Litecoin, the generalized hyperbolic distribution gives the best fit, while for the smaller cryptocurrencies the normal inverse Gaussian distribution, generalized t distribution, and Laplace distribution give good fits. The results are important for investment and risk management purposes.

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Section: Introductionmentioning

confidence: 99%

A Statistical Analysis of Cryptocurrencies

Chan¹,

Chu²,

Nadarajah³

et al. 2017

JRFM

Self Cite

142

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“…Two recent papers on fitting of distributions to exchange rate data (traditional fiat currencies) are [3] and [4]. [3] fitted the generalized Lambda, skew t, normal inverse Gaussian and normal distributions as well as the Johnson's family of distributions to the data.…”

Section: Heavy-tailed Distributionsmentioning

confidence: 99%

The Statistics of Bitcoin and Cryptocurrencies

Osterrieder

2016

SSRN Journal

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Cryptocurrencies became popular with the emergence of Bitcoin and have shown an unprecedented growth over the last few years. As of November 2016, more than 720 cryptocurrencies exist, with Bitcoin still being the most popular one. We show the statistical properties of the most important cryptocurrencies. We characterize their exchange rates versus the US Dollar by fitting parametric distributions to them, including the Student t distribution, the generalized hyperbolic distribution as well as the asymmetric normal inverse Gaussian and the asymmetric variance gamma distribution. Our findings show that cryptocurrencies exhibit strong non-normal characteristics, with standard heavy-tailed distributions such as the Student t distribution giving good descriptions of the data. This is the first study that looks at the parametric distribution of cryptocurreny returns. The results are important for investment and risk management purposes.

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“…Although less tractable than the Gaussian, this distribution has also frequently appeared as a convenient alternative for describing the log returns of different assets. In particular, in Blattberg & Gonedes (1974) it was used for modeling stock dynamics, in Nadarajah et al (2015) for currencies, while Platen & Rendek (2008) have implemented it for modeling the returns of market indexes. Moreover, it was used for study of joint distribution by Chicheportiche & Bouchaud (2012) and it was obtained that it can provide a good fit for strongly correlated stocks.…”

Section: Introductionmentioning

confidence: 99%

Option Pricing With Heavy-Tailed Distributions of Logarithmic Returns

Basnarkov

Stojkoski

Utkovski

et al. 2019

Int. J. Theor. Appl. Finan.

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A growing body of literature suggests that heavy tailed distributions represent an adequate model for the observations of log returns of stocks. Motivated by these findings, here we develop a discrete time framework for pricing of European options. Probability density functions of log returns for different periods are conveniently taken to be convolutions of the Student's t-distribution with three degrees of freedom. The supports of these distributions are truncated in order to obtain finite values for the options. Within this framework, options with different strikes and maturities for one stock rely on a single parameter -the standard deviation of the Student's t-distribution for unit period. We provide a study which shows that the distribution support width has weak influence on the option prices for certain range of values of the width. It is furthermore shown that such family of truncated distributions approximately satisfies the no-arbitrage principle and the put-call parity. The relevance of the pricing procedure is empirically verified by obtaining remarkably good match of the numerically computed values by our scheme to real market data.

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A note on “Modelling exchange rate returns: which flexible distribution to use?”

Cited by 15 publications

References 21 publications

A Statistical Analysis of Cryptocurrencies

A Statistical Analysis of Cryptocurrencies

The Statistics of Bitcoin and Cryptocurrencies

Option Pricing With Heavy-Tailed Distributions of Logarithmic Returns

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