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Zusatztext "?a suitable text for an advanced undergraduate or graduate-level course in option valuation via the binomial model and the Black-Scholes-Merton model."-International Statistical Review! 2013"The text provides an introduction to classical material of mathematical finance! i.e. the notions of arbitrage! replication! and option pricing in the context of the discrete-time Cox-Ross-Rubinstein and the continuous-time Black-Scholes model! respectively. The book sticks out by not assuming any background in stochastics. All necessary concepts of probability theory! martingales! and Itô calculus are provided ?"-Jan Kallsen! Zentralblatt MATH 1247 Informationen zum Autor Hugo D. Junghenn is a professor of mathematics at the George Washington University. His research interests include functional analysis and semigroups. Klappentext This book provides a mathematically rigorous! straightforward account of option pricing in financial mathematics. The author treats the intricate financial models in a direct way that can be understood by those with only a calculus prerequisite. He also includes an in-depth discussion of probability theory! martingale methods! and the use of spreadsheets to give numerical substance to the theoretical models. The text contains numerous examples and exercises that range from fairly routine to the pricing of complex financial instruments! helping readers gain expertise in financial calculus methods. Zusammenfassung Option Valuation: A First Course in Financial Mathematics provides a straightforward introduction to the mathematics and models used in the valuation of financial derivatives. It examines the principles of option pricing in detail via standard binomial and stochastic calculus models. Developing the requisite mathematical background as needed! the text presents an introduction to probability theory and stochastic calculus suitable for undergraduate students in mathematics! economics! and finance.The first nine chapters of the book describe option valuation techniques in discrete time! focusing on the binomial model. The author shows how the binomial model offers a practical method for pricing options using relatively elementary mathematical tools. The binomial model also enables a clear! concrete exposition of fundamental principles of finance! such as arbitrage and hedging! without the distraction of complex mathematical constructs. The remaining chapters illustrate the theory in continuous time! with an emphasis on the more mathematically sophisticated Black-Scholes-Merton model.Largely self-contained! this classroom-tested text offers a sound introduction to applied probability through a mathematical finance perspective. Numerous examples and exercises help students gain expertise with financial calculus methods and increase their general mathematical sophistication. The exercises range from routine applications to spreadsheet projects to the pricing of a variety of complex financial instruments. Hints and solutions to odd-numbered problems are given in an appendix and a full solutions manual is available for qualifying instructors. Inhaltsverzeichnis Interest and Present ValueCompound Interest Annuities Bonds Rate of ReturnProbability SpacesSample Spaces and Events Discrete Probability Spaces General Probability Spaces Conditional Probability IndependenceRandom VariablesDefinition and General Properties Discrete Random Variables Continuous Random Variables Joint Distributions Independent Random Variables Sums of Independent Random VariablesOptions and ArbitrageArbitrage Classification of Derivatives Forwards Currency Forwards FuturesOptions Properties of Options Dividend-Paying StocksDiscrete-Time Portfolio ProcessesDiscrete-Time Stochastic ProcessesSelf-Financing Portfolios Option Valuation by PortfoliosExpectation of a Random VariableDiscrete Case: Definition and Examples Continuous C...
