Lewis A.L., Option Valuation under Stochastic Volatility

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...

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...

Contents. Gaussian Stochastic Calculus of Variations. Finite-Dimensional Gaussian Spaces. Hermite Expansion. Wiener Space as Limit of its Dyadic Filtration. Stroock–Sobolev Spaces. of Functionals on Wiener Space. Divergence of Vector Fields, Integration by Parts. It?o’s Theory of Stochastic Integrals. Differential and Integral Calculus. in Chaos Expansion. Monte-Carlo Computation of Divergence. Computation of Greeks. and Integration by Pa...

© 2009 by the Society for Industrial and Applied Mathematics. Contents. Preface. List of Algorithms. Financial Indices Appear to Be Stochastic Processes. Brownianmotionis alsocalledaWienerprocess. Stochastic drift and volatility are unique. Basic numerics simulate anSDE. A binomial lattice prices call option. Summary. Exercises. Ito’s Stochastic Calculus Introduced. Multiplicative noise reduces exponential growth. Ito’s formulasolves som...

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...

Academic Press; 2 edition (December 15, 2008), 696 страниц Язык: English ISBN-10: 0123735742 ISBN-13: 978-0123735744 Cash Flow Engineering and Forward Contracts Engineering Simple Interest Rate Derivatives Introduction to Swap Engineering Repo Market Strategies in Financial Engineering Dynamic Replication Methods and Synthetics Mechanics of Options Engineering Convexity Positions Options Engineering with Applications Pricing Tools in Fi...

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...

N.-Y., John Wiley & Sons, 1996. - 515p. This book is about hedging the risks of standard and exotic options, as part of the larger framework of risk management. No road map was available since little has been written on this subject (in contrast to the extensive literature for valuation). ‘‘Dynamic hedging’’ is more like medicine than biology. It is learned by gaining practical experience as well as by studying published research. The wrink...

One mathematical and financial foundations. Basic theory of derivatives. Risk and return. Products and Markets. Derivatives. The Random Behavior of Assets. Elementary Stochastic Calculus. The Black–Scholes Model. al Differential Equations. The Black–Scholes Formulae and the ‘Greeks’. Simple Generalizations of the Black–Scholes World. Early Exercise and American Options. Probability Density Functions and First-exit times. Multi-asset Options. Ho...