Contingent Claim Pricing Using a Normal Inverse Gaussian Probability Distortion Operator

26 Pages Posted: 23 Aug 2012

See all articles by Frédéric Godin

Frédéric Godin

Concordia University, Quebec - Department of Mathematics & Statistics; Université Laval

Silvia Mayoral

Universidad Carlos III de Madrid

Manuel Morales

University of Montreal

Date Written: September 2012

Abstract

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.

Suggested Citation

Godin, Frédéric and Mayoral, Silvia and Morales, Manuel, Contingent Claim Pricing Using a Normal Inverse Gaussian Probability Distortion Operator (September 2012). Journal of Risk and Insurance, Vol. 79, Issue 3, pp. 841-866, 2012. Available at SSRN: https://ssrn.com/abstract=2134739 or http://dx.doi.org/10.1111/j.1539-6975.2011.01445.x

Frédéric Godin (Contact Author)

Concordia University, Quebec - Department of Mathematics & Statistics ( email )

1455 De Maisonneuve Blvd. W.
Montreal, Quebec H3G 1M8
Canada

Université Laval ( email )

2214 Pavillon J-A. DeSeve
Quebec, Quebec G1K 7P4
Canada

Silvia Mayoral

Universidad Carlos III de Madrid ( email )

C/ Madrid 124,
Getafe, Madrid 28093
Spain

Manuel Morales

University of Montreal ( email )

C.P. 6128 succursale Centre-ville
Montreal, Quebec H3C 3J7
Canada

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