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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