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A numerical study of adjusted parameter estimation in normal inverse Gaussian distribution
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 Title & Authors
A numerical study of adjusted parameter estimation in normal inverse Gaussian distribution
Yoon, Jeongyoen; Song, Seongjoo;
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Numerous studies have shown that normal inverse Gaussian (NIG) distribution adequately fits the empirical return distribution of financial securities. The estimation of parameters can also be done relatively easily, which makes the NIG distribution more useful in financial markets. The maximum likelihood estimation and the method of moments estimation are easy to implement; however, we may encounter a problem in practice when a relationship among the moments is violated. In this paper, we investigate this problem in the parameter estimation and try to find a simple solution through simulations. We examine the effect of our adjusted estimation method with real data: daily log returns of KOSPI, S&P500, FTSE and HANG SENG. We also checked the performance of our method by computing the value at risk of daily log return data. The results show that our method improves the stability of parameter estimation, while it retains a comparable performance in goodness-of-fit.
normal inverse Gaussian distribution;feasible domain;parameter estimation;Value at Risk;
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Barndorff-Nielsen, O. E. (1977). Exponentially decreasing distributions for the logarithm of particle size. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 353, 401-419. crossref(new window)

Barndorff-Nielsen, O. E. (1997). Processes of normal inverse gaussian type, Finance and Stochastics, 2, 41-68. crossref(new window)

Barndorff-Nielsen, O. E., Blaesild, P., Jensen, J. L., and Sorensen, M. (1985). The Fascination of Sand, Springer, 57-87.

Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities, The Journal of Political Economy, 2, 637-654.

Carr, P., Geman, H., Madan, D., and Yor, M. (2002). The fine structure of asset returns: an empirical investigation, Journal of Business, 75, 305-333. crossref(new window)

Clark, P. K. (1973). A subordinated stochastic process model with finite variance for speculative prices, Econometrica, 41, 135-155. crossref(new window)

Cox, J. and Ross, S. (1976). The valuation of options for alternative stochastic processes, Journal of Financial Economics, 3, 145-166. crossref(new window)

Eriksson, A., Ghysels, E., and Wang, F. (2009). The normal inverse Gaussian distribution and the pricing of derivatives, The Journal of Derivatives, 16, 23-37. crossref(new window)

Fielitz, B. D. and Smith, E. W. (1972). Asymmetric stable distributions of stock price changes, Journal of the American Statistical Association, 67, 813-814. crossref(new window)

Figueroa-Lopez, J. E., Lancette, S. R., Lee, K., and Mi, Y. (2011). Estimation of NIG and VG models for high frequency financial data, Handbook of Modeling High-Frequency Data in Finance, John Wiley & Sons, 3-26.

Geman, H. (2002). Pure jump Levy processes for asset price modeling, Journal of Banking and Finance, 26, 1297-1316. crossref(new window)

Ghysels, E. and Wang, F. (2014). Moment-implied densities: properties and applications, Journal of Business & Economic Statistics, 32, 88-111. crossref(new window)

Hull, J. and White, A. (1987). The pricing of options on assets with stochastic volatilities, The Journal of Finance, 42, 281-300. crossref(new window)

Kim, T. and Song, S. (2011). Value-at-Risk Estimation using NIG and VG Distribution, Journal of the Korean Data Analysis Society, 13, 1775-1788.

Kupiec, P. H. (1995). Techniques for verifying the accuracy of risk measurement models, The Journal of Derivatives, 3, 73-84. crossref(new window)

Madan, D. and Seneta, E. (1990). The VG model for share market returns, Journal of Business, 63, 511-524. crossref(new window)

Mandelbrot, B. (1963). The variation of certain speculative prices, Journal of Business, 36, 394-419. crossref(new window)

Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, 3, 125-144. crossref(new window)

Prause, K. (1997). Modelling financial data using generalized hyperbolic distributions, FDM Preprint, 48, University of Freiburg.