Normal inverse Gaussian

IJMwaniki. "On skewed leptokurtic returns and pentanomial lattice option valuation via minimal entropy martingale measure." Cogent Economics & Finance. 2017;5(1):1-16. AbstractWebsite

This article develops, a lattice-based approach for pricing contingent claims when parameters governing the logs of the underlying asset dynamics are modelled by generalized hyperbolic distribution and normal inverse Gaussian distribution. The pentanomial lattice is constructed using a moment matching procedure. Moment generating functions of generalized hyperbolic distribution and normal inverse Gaussian distribution are utilized to compute probabilities and jump parameters under historical measure P. Minimal entropy martingale measure (MEMM) is used to value European call option with a view of comparing the results with some of the existing benchmark models such as Black Scholes model. Empirical data from S&P500 index, RUTSELL2000 index and RUI1000 index are used to demonstrate how the model works. There is a significant difference especially for long term maturity (six months and above) type of contracts, the proposed model outperform the benchmark model, while performing poorly at short term contracts. Pentanomial NIG models seem to outperform the other models, especially for long-dated maturities.

IJMwaniki. "Modeling heteroscedastic, skewed and leptokurtic returns in discrete time." Journal of Applied Finance & Banking. 2019;9(5):1-14. AbstractWebsite

Popular models of finance, fall short of accounting for most empirically found stylized features of financial time series data, such as volatility clustering, skewness and leptokurtic nature of log returns. In this study, we propose a general framework for modeling asset returns which account for serial dependencies in higher moments and leptokurtic nature of scaled GARCH filtered residuals. Such residuals are calibrated to normal inverse Gaussian and hyperbolic distribution. Dynamics of risky assets assumed in Black Scholes model, Duans GARCH model and other benchmark models for contract valuation, are shown to be nested in the the proposed framework

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