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Econophysics & Stylized Facts of Financial Stock Markets & Nonextensive Derivative Pricing Formulas. Doctoral Thesis Of Fredrick Michael, PhD

Fredrick Michael

posted on 21 February 2018

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Doctoral Thesis of Fredrick N. Michael, PhD 2002. The PhD thesis covers a dual track candidacy. The first relating to condensed matter theoretical physics, nanometer scale structures, transport, interactions and fields where quantum effects dominate. We obtain detailed descriptions via NEGF non equilibrium Green's functions of quantum non equilibrium transport, coupling of materials, effects of external fields that model spintronics, ballistic transport, and quantum multilayered structures in general.
The second part of the thesis applies the Non extensive entropy and statistics of C. Tsallis to complex and random systems. Specifically we find a nearly perfect stochastic, and statistics of the US S&P500 Standard and Poor's high frequency 500 stocks index and extrapolate to open complex systems inclusive of financial markets in general. Additionally having obtained a highly accurate stochastic differential equation(s) and PDE partial differential equation of the financial market, we generalize the Black-Scholes derivatives pricing theory and formula to the nonextensive statistics accounting for accuracy of the description of the trajectory of the underlying random assets and therefore a highly accurate European style option pricing formula.

 

Keywords: condensed matter, theory, self energy, coupling, non equilibrium, statistics, statistical mechanics, quantum , classical, non extensive, nonextensive, multi layer, spintronics, NEGF non equilibrium Green's functions, ballistic transport, heterostructures, financial markets, stochastic, Ito , nonlinear partial differential equations, Tsallis-Zanette PDE, Fokker-Planck.