Extended Kalman-filter, Taylor–Heun-integration, Modified Gauss–Legendre-formula,

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This new and exciting book offers a fresh approach to quantitative inance and utilizes novel new features, including stereoscopic images which permit 3D visualization of complex subjects without the need for additional tools.Offering an integrated approach to the subject, A First Course in Quantitative Finance introduces students to the architecture of complete inancial markets before exploring the concepts and models of modern portfolio theory, derivative pricing, and ixed-income products in both complete and incomplete market settings. Subjects are organized throughout in a way that encourages a gradual and parallel learning process of both the economic concepts and their mathematical descriptions, framed by additional perspectives from classical utility theory, inancial economics, and behavioral inance.Suitable for postgraduate students studying courses in quantitative inance, inancial engineering, and inancial econometrics as part of an economics, inance, econometric, or mathematics program, this book contains all necessary theoretical and mathematical concepts and numerical methods, as well as the necessary programming code for porting algorithms onto a computer.Professor Dr. Thomas Mazzoni has lectured at the University of Hagen and the Dortmund Business School and is now based at the University of Greifswald, Germany, where he received the 2014 award for excellence in teaching and outstanding dedication. Cambridge University Press

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This paper introduces a new method for pricing European style call options with GARCH models. The resulting pricing formula is an explicit function of the model parameters, current spot asset price, exercise price and time to maturity. The method under consideration is remarkably fast because no numerical integration procedures are involved. Errors, resulting from approximation and series expansion, are surveyed by Monte-Carlo methods and turn out to be negligible.