Risk managers must build models from data in order to asses risk. A part of my research program involves studying risk measures that take data directly as input without further model assumptions. Data-based risk measures can be coherently defined from a set of axioms yielding interesting families.
We consider the problem of pricing contingent claims using distortion operators. This approach was first developed in (Wang, 2000) where the original distortion function was defined in terms of the normal distribution. Here, we introduce a new distortion based on the Normal Inverse Gaussian (NIG) distribution. The NIG is a generalization of the normal distribution that allows for heavier skewed tails. The resulting operator asymmetrically distorts the underlying distribution.
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