Borak S., Detlefsen K., Hardle W. FFT Based Option Pricing

Designed to form the basis of an undergraduate course in mathematical finance, this book builds on mathematical models of bond and stock prices and covers three major areas of mathematical finance that all have an enormous impact on the way modern financial markets operate, namely: Black-Scholes’ arbitrage pricing of options and other derivative securities; Markowitz portfolio optimization theory and the Capital Asset Pricing Model; and interest...

Society for Industrial and Applied Mathematics, 2005, -316 pp. Mathematical finance is an old science but has become a major topic for numerical analysts since Merton [97], Black-Scholes [16] modeled financial derivatives. An excellent book for the mathematical foundation of option pricing is Lamberton and Lapeyre's [85]. Since the Black-Scholes model relies on stochastic differential equations, option pricing rapidly became an attractive topic...

Steven E. Shreve, 1997. - 347 pages. Contens: Introduction to Probability Theory Conditional Expectation Arbitrage Pricing The Markov Property Stopping Times and American Options Properties of American Derivative Securities Jensen’s Inequality Random Walks Pricing in terms of Market Probabilities: The Radon-Nikodym Theorem. Capital Asset Pricing General Random Variables Semi-Continuous Models Brownian Motion The Ito Integral Ito’s Formula...

N.-Y., McGrow Hill, 1998. - 572p. Справочник по расчёту цен опционов и производных показателей ("греков"), включая опционы американского стиля, экзотические опционы на один или два актива, альтернативные формуле Блэка-Шоулса методы расчёта, методы на основе уравнений с частными производными и Монте-Карло, учёт дивидендных выплат, опционы на товары, энергию и ставку процента. Рассматриваются понятия волатильности и корреляции и их влияния на цену...

M.S. Joshi, 2008. - 538 pages. An ideal introduction for those starting out as practitioners of mathematical finance, this book provides a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice. Strengths and weaknesses of different models, e.g. Black-Scholes, stochastic volatility, jump-diffusion and variance gamma, are examined. Both the theory and the implemen...

University of Minnesota, 2000. Contents I Equilibrium and Arbitrage 1 Equilibrium in Security Markets 2 Linear Pricing 3 Arbitrage and Positive Pricing 4 Portfolio Restrictions II Valuation 5 Valuation 6 State Prices and Risk-Neutral Probabilities 7 Valuation under Portfolio Restrictions III Risk 8 Expected Utility 9 Risk Aversion 10 Risk IV Optimal Portfolios V Equilibrium Prices and Allocations VI Mean-Variance Analysis VII Multidate Se...

Unlike most books on investments, financial engineering, or derivative securities, the book starts from basic ideas in finance and gradually builds up the theory. Modern Finance:A Brief History Financial Engineering and Computation Financial Markets Computer Technology Analysis of Algorithms Complexity Analysis of Algorithms Description of Algorithms Software Implementation Basic Financial Mathematics Bond Price Volatility Term Structure of Inte...

Cambridge University Press, 2011. - 328 pages. This textbook on the basics of option pricing is accessible to readers with limited mathematical training. It is for both professional traders and undergraduates studying the basics of finance. Assuming no prior knowledge of probability, Sheldon M. Ross offers clear, simple explanations of arbitrage, the Black-Scholes option pricing formula, and other topics such as utility functions, optimal portf...

The notes are based on courses offered regularly to graduate students in economics and mathematics at the University of Bonn choosing financial economics as special topic. To students interested in finance the course opens a quick (but by no means dirty) road to the tools required for advanced finance. One can start the course with what they know about real analysis (e.g. Taylor’s Theorem) and basic probability theory as usually taught in undergr...

John Wiley & Sons, Inc., 2002. – 304 pages. This book is designed as a graduate textbook in financial engineering. It was motivated by the need to present the main techniques used in quantitative pricing in a single source adequate for Master level students. Students are expected to have some background in algebra, elementary statistics, calculus, and elementary techniques of financial pricing, such as binomial trees and simple Monte Carlo s...