The hyperbolic model: Option pricing using approximation and Quasi-Monte Carlo methods

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The dissertation explores the mathematical significance of options, building on the foundational work of Black and Scholes while challenging their assumption of normally distributed log-returns. It adopts the hyperbolic distribution model proposed by Eberlein and Keller, expanding the analysis to include Asian, American, and multi-asset options. The research extends the standard martingale measure through an entropy-minimizing approach, acknowledging the impossibility of exact pricing for these options. Instead, it employs numerical simulations, including Monte Carlo methods with variance reduction techniques and quasi-Monte Carlo methods.