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    An analysis of snow options for ski resort establishments
    (Elsevier Sci Ltd, 2010) Beyazit, Mehmet Fuat; Koc, Erdogan
    This study proposes a pricing method for put options on snow level for tourism establishments operating in Palandoken ski resort in the east of Turkey. In the calculation of put prices historical densities and Edgeworth adjusted densities methods together with Alaton, Djehiche, and Stillberger (2002) method have been applied. The findings show that there may be significant differences in the prices calculated by the three different methods, hence enabling both parties, i.e. buyers and sellers, with bases in the negotiation process. As the study is primarily aimed at providing a framework for pricing put options on snow levels in general, it is expected that it would be of use not only for this particular ski resort but also for various ski resorts in the world. (C) 2009 Elsevier Ltd. All rights reserved.
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    Lewis Model Revisited: Option Pricing with Levy Processes
    (Malaysian Mathematical Sciences Soc, 2021) Beyazit, Mehmet Fuat; Eroglu, Kemal Ilgar
    This paper aims to discuss the mathematical details in Lewis' model by considering the analyticity and integrability conditions of characteristic functions and payoff functions of contingent claims. In his seminal paper, Lewis shows that it is much easier to compute the option value in the Fourier space than computing in terminal security price space. He computes the option value as an integral in the Fourier space, the integrand being some elementary functions and the characteristic functions of a wide range of Levy processes. The model also illustrates how the residue calculus leads to several variations of option formulas through the contour integrals. In this paper, we provide with, to a reasonable extent, some rigor into the mathematical background of Lewis' model and validate his results for particular Levy processes. We also simply give the analyticity conditions for the characteristic function of the Carr-Geman-Madan-Yor model and a simple derivation of the characteristic function of Kou's double exponential model.
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    The Mathematical Aspects of Barrier Options
    (World Scientific Publishing Co., 2025) Beyazit, Mehmet Fuat
    This book explains the types of barrier options that are widely traded in Over-the-Counter (OTC) markets and secondary markets. The main objective of the book is to analyze the basic pricing formulae of the different types of barrier options and to produce comprehensive, detailed and explanatory derivations of the pricing formulae. The book is also aimed at practitioners working in the financial world. The detailed derivation of the formulae will enable the finance practitioners to understand sophisticated financial products better. Also, the book gives the methods on how to hedge the barrier options which are the risky instruments for the writers/ practitioners, particularly when the underlying variable is at the neighborhood of the barrier. It is also expected that the approach, and especially the clearly applied methods in deriving partial barriers, will help broaden the perspectives of students and academics interest in this subject. © 2026 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.