Financial Derivative and Energy Market Valuation: Theory and Implementation in MATLAB

Preface

Energy markets and their associated financial derivatives are characterized by sudden jumps, mean reversion, and stochastic volatility. These aspects necessitate sophisticated models to properly describe even a subset of these traits. Moreover, the implementation of these models itself requires advanced numerical methods. This book establishes the fundamental mathematics and builds up all necessary statistical, quantitative, and financial theories.

A number of theoretical topics are expanded, including the Fourier transform, moment generating functions, characteristic functions, and finite and infinite activity Levy processes such as the alpha stable, tempered stable, gamma, variance gamma, inverse Gaussian, and normal inverse Gaussian processes. Applied mathematics such as the fast Fourier transform and the fractional fast Fourier transform are developed and used to generate statistical distributions and for option pricing.

On the basis of this knowledge, state-of-the-art quantitative financial models are developed without the need to refer external sources. Seminal works are derived and implemented, including the Black–Scholes, Black, Ornstein–Uhlenbeck, Merton Gaussian jump diffusion, Kou double exponential jump diffusion, and Heston stochastic volatility models.

Nevertheless, these models cannot capture the true behavior of the energy markets. The influential two-factor stochastic convenience yield model and the short-term long-term model are derived and implemented. ...