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Underlying Assets Distribution in Derivatives: The BRIC Case

DOI: 10.4236/tel.2018.83035, PP. 502-513

Keywords: Derivatives, Normal Inverse Gaussian, Valuation, Returns, BRIC

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This paper addresses one of the main issues regarding numerical derivatives valuation, particularly the search for an alternative to the normality assumption of underlying asset returns, to obtain the price by using numerical techniques. There might be difficulties in making normality assumptions, which could produce over-valuated or sub-valuated prices of derivatives. Under this consideration, the Generalized Hyperbolic family has been proven to be a proper selection to model heavy tailed distribution behavior. The Normal Inverse Gaussian (NIG) distribution is a member flexible enough to model financial returns. NIG distribution can be used to model distribution returns under different states of nature. The indexes of the Brazil, Russia, India and China (BRIC) economies were studied at different time-periods using return data series from 2002 to 2005, 2006 to 2010 and 2011 to 2015, in such a manner to demonstrate with statistical criteria that NIG fits the empirical distribution in the three periods; even throughout economic downturn. This result may be used as an improvement in derivatives valuation with indexes as underlying assets.


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