Normal Inverse Gaussian Model Research Articles

Volatility Smile Surface for Levy Option Pricing Model

This paper discusses theoretical extensions of the implied volatility method of Dupire (1994) when the stock prices follow the Geometric Levy process. For the extensions of Kolmogorov forward equation for Levy process, this paper uses adjoint operator in L² spaces. This paper obtains similar results of Dupire (1994) and Andersen and Andreasan (2001). However, our results can be applied to more general semi-martingale processes such as well-known VG (Variance Gamma) model and NIG (Normal Inverse Gaussian) model with diffusion processes. This paper also applies the approach to the case of stochastic time changed Levy process, which generates the stochastic volatility models.

A NOTE ON PORTFOLIO MANAGEMENT UNDER NON-GAUSSIAN LOGRETURNS

We calculate numerically the optimal allocation and consumption strategies for Merton's optimal portfolio management problem when the risky asset is modelled by a geometric normal inverse Gaussian Lévy process. We compare the computed strategies to the ones given by the standard asset model of geometric Brownian motion. To have realistic parameters in our studies, we choose Norsk Hydro quoted on the New York Stock Exchange as the risky asset. We find that an investor believing in the normal inverse Gaussian model puts a greater fraction of wealth into the risky asset. We also investigate the limiting investment rate when the volatility increases. We observe different behaviour in the two models depending on which parameters we vary in the normal inverse Gaussian distribution.

Convergence of Distributions Generated by Stationary Stochastic Processes

Convergence of Distributions Generated by Stationary Stochastic Processes