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The Normal Inverse Gaussian Distribution and the Pricing of Derivatives

The authors propose the class of normal inverse gaussian (NIG) distributions to approximate an unknown risk-neutral density. The appeal of the NIG class of distributions is that it is characterized by the first four moments: mean, variance, skewness, and kurtosis. These are the moments that are important to many risk management applications. One strength of this approach is that the authors link the pricing of individual derivatives to the moments of the risk-neutral distribution, which has an intuitive appeal in terms of how volatility, skewness, and kurtosis of the risk-neutral distribution can explain the behavior of derivative prices. The authors provide numerical and empirical evidence showing appealing features of their approach, notably its superior performance compared to the existing methods.