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Contingent Claim Pricing Using a Normal Inverse Gaussian Probability Distortion Operator
Author(s) -
Godin Frédéric,
Mayoral Silvia,
Morales Manuel
Publication year - 2012
Publication title -
journal of risk and insurance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.055
H-Index - 63
eISSN - 1539-6975
pISSN - 0022-4367
DOI - 10.1111/j.1539-6975.2011.01445.x
Subject(s) - inverse gaussian distribution , distortion (music) , gaussian , normal inverse gaussian distribution , distortion function , normal distribution , generalization , generalized inverse gaussian distribution , operator (biology) , mathematics , inverse , distribution (mathematics) , mathematical economics , computer science , mathematical analysis , gaussian process , algorithm , statistics , gaussian random field , physics , telecommunications , quantum mechanics , repressor , amplifier , chemistry , decoding methods , bandwidth (computing) , biochemistry , geometry , transcription factor , gene
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. Moreover, we show how we can recuperate non‐Gaussian Black–Scholes formulas using distortion operators and we provide illustrations of their performance. We conclude with a brief discussion on risk management applications.