Very few models allow expressing European call option price in closed form. Out of them, the famous Black- Scholes approach sets strong constraints - innovations should be normally distributed and independent. Availability of a corresponding characteristic function of log returns of underlying asset in analytical form allows pricing European call option by application of inverse Fourier transform. Characteristic function corresponds to Normal Inverse Gaussian (NIG) probability density function. NIG distribution is obtained based on assumption that time series of log returns follows APARCH process. Thus, volatility clustering and leptokurtic nature of log returns are taken into account. The Fast Fourier transform based on trapezoidal quadrature is numerically unstable if a standard cumulative probability function is used. To solve the problem, a dampened cumulative probability is introduced. As a computation tool Matlab framework is chosen because it contains many effective vectorization tools that greatly enhance code readability and maintenance. The characteristic function of Normal Inverse Gaussian distribution is taken and exercised with the chosen set of parameters. Finally, the call price dependence on strike price is obtained and rendered in XY plot. Valuation of European call option with analytical form of characteristic function allows further developing models with higher accuracy, as well as developing models for some exotic options.
 K. Chourdakis, “Financial Engineering, A brief introduction using the Matlab system,” 2008 [Online]. Available: http://cosweb1.fau.edu/~jmirelesjames/MatLabCode/Lecture_notes_2008d.pdf
 K. K. Sæbø, Pricing Exotic Options with the Normal Inverse GaussianMarket Model using Numerical Path Integration, 2009.
 F. D. Rouah, “Four derivations of the Black Scholes equation PDE,”[Online]. Available: http://www.frouah.com/finance%20notes/Black%20Scholes%20PDE.pdf
 O. Calin, An Informal Introduction to Stochastic Calculus with Applications, 2015. https://doi.org/10.1142/9620
 S. Shreve, Stochastic Calculus and Finance, 1997.
 A. K. Diongue and D. Guégan, “The stationary seasonal hyperbolic asymmetric power ARCH model,” Statistics & Probability Letters, vol. 77, no. 11, pp. 1158-1164, Jun. 2007. https://doi.org/10.1016/j.spl.2007.02.007
 D. Edwards, “Numerical and analytic methods in option pricing,” 2015.
 T. Mazzoni, “Zeitreihenanalyse, Einstieg und Aufgaben,” [Online]. Available: http://www.fernuni-hagen.de/imperia/md/content/ls_statistik/zeitreihenskript_als_ke2.pdf
 O. E. Barndorff-Nielsen, “Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling,” Scandinavian Journal of Statistics, vol. 24, no. 1, pp. 1-13, Mar. 1997. https://doi.org/10.1111/1467-9469.t01-1-00045
 I. J. Mwaniki, “Modeling Returns and Unconditional Variance in Risk Neutral World for Liquid and Illiquid Market,” Journal of Mathematical Finance, vol. 05, no. 01, pp. 15-25, 2015. https://doi.org/10.4236/jmf.2015.51002
 P. Carr and D. Madan, “Option valuation using the fast Fourier transform,” The Journal of Computational Finance, vol. 2, no. 4, pp. 61-73, 1999. https://doi.org/10.21314/jcf.1999.043
 M. Karanasos and J. Kim, “A re-examination of the asymmetric power ARCH model,” Journal of Empirical Finance, vol. 13, no. 1, pp. 113-128, Jan. 2006. https://doi.org/10.1016/j.jempfin.2005.05.002