Abstract
The normal-Laplace (NL) distribution results from convolving independent normally distributed and Laplace distributed components. It is the distribution of the stopped state of a Brownian motion with a normally distributed starting value if the stopping hazard rate is constant. Properties of the NL distribution discussed in the article include its shape and tail behaviour (fatter than the normal), its moments, and its infinite divisibility. The double Pareto-lognormal distribution is that of an exponentiated normal-Laplace random variable and provides a useful parametric form for modelling size distributions. The generalized normal-Laplace (GNL) distribution is both infinitely divisible and closed under summation. It is possible to construct a Lévy process whose increments follow the GNL distribution. Such a Lévy motion can be used to model the movement of the logarithmic price of a financial asset. An option pricing formula is derived for such an asset.
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References
Barndorff-Nielsen, O. E. (1977). Exponentially decreasing distributions for the logarithm of particle size, Proceedings of the Royal Society of London, Series A, 353, 401–419.
Barndorff-Nielsen, O. E. (1997). Normal inverse Gaussian distributions and stochastic volatility models, Scandinavian Journal of Statistics, 24, 1–13.
Eberlein, E., and Keller, U. (1995). Hyperbolic distributions in finance, Bernoulli, 1, 281–289.
Kotz, S., Kozubowski, T. J., and Podgórski, K. (2001). The Laplace Distribution and Generalizations, Birkhäuser, Boston.
Reed, W. J., and Jorgensen, M. (2004). The double Pareto-lognormal distribution: A new parametric model for size distributions, Communications in Statistics—Theory and Methods, 33, 1733–1753.
Rydberg, T. H. (2000). Realistic statistical modelling of financial data, International Statistical Review, 68, 233–258.
Schoutens, W. (2003). Lévy Processes in Finance, John Wiley_& Sons, Chichester.
Wilson, E. B. (1923). First and second laws of error, Journal of the American Statistical Association, 18, 841–852.
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© 2006 Birkhäuser Boston
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Reed, W.J. (2006). The Normal-Laplace Distribution and Its Relatives. In: Balakrishnan, N., Sarabia, J.M., Castillo, E. (eds) Advances in Distribution Theory, Order Statistics, and Inference. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4487-3_4
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DOI: https://doi.org/10.1007/0-8176-4487-3_4
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