Mathematics of financial markets [electronic resource] /
Elliott, Robert J.(Robert James),1940-
Kopp, P. E.,1944-
New York, N.Y. : Springer,
2005.
This book presents the mathematics that underpins pricing models for derivative securities, such as options, futures and swaps, in modern financial markets. The idealized continuous-time models built upon the famous Black-Scholes theory require sophisticated mathematical tools drawn from modern stochastic calculus. However, many of the underlying ideas can be explained more simply within a discrete-time framework. This is developed extensively in this substantially revised second edition to motivate the technically more demanding continuous-time theory, which includes a detailed analysis of the Black-Scholes model and its generalizations, American put options, term structure models and consumption-investment problems. The mathematics of martingales and stochastic calculus is developed where it is needed. The new edition adds substantial material from current areas of active research, notably :a new chapter on coherent risk measures, with applications to hedging; a complete proof of the first fundamental theorem of asset pricing for general discrete market models; the arbitrage interval for incomplete discrete-time markets; characterization of complete discrete-time markets, using extended models; risk and return and sensitivity analysis for the Black-Scholes model. The treatment remains careful and detailed rather than comprehensive, with a clear focus on options. From here the reader can progress to the current research literature and the use of similar methods for more exotic financial instruments. The text should prove useful to graduates with a sound mathematical background, ideally a knowledge of elementary concepts from measure-theoretic probability, who wish to understand the mathematical models on which the bewildering multitude of current financial instruments used in derivative markets and credit institutions is based. The first edition has been used successfully in a wide range of Master’s programs in mathematical finance and this new edition should prove even more popular in this expanding market. It should equally be useful to risk managers and practitioners looking to master the mathematical tools needed for modern pricing and hedging techniques.
Includes bibliographical references and index.
This book presents the mathematics that underpins pricing models for derivative securities, such as options, futures and swaps, in modern financial markets. The idealized continuous-time models built upon the famous Black-Scholes theory require sophisticated mathematical tools drawn from modern stochastic calculus. However, many of the underlying ideas can be explained more simply within a discrete-time framework. This is developed extensively in this substantially revised second edition to motivate the technically more demanding continuous-time theory, which includes a detailed analysis of the Black-Scholes model and its generalizations, American put options, term structure models and consumption-investment problems. The mathematics of martingales and stochastic calculus is developed where it is needed. The new edition adds substantial material from current areas of active research, notably :a new chapter on coherent risk measures, with applications to hedging; a complete proof of the first fundamental theorem of asset pricing for general discrete market models; the arbitrage interval for incomplete discrete-time markets; characterization of complete discrete-time markets, using extended models; risk and return and sensitivity analysis for the Black-Scholes model. The treatment remains careful and detailed rather than comprehensive, with a clear focus on options. From here the reader can progress to the current research literature and the use of similar methods for more exotic financial instruments. The text should prove useful to graduates with a sound mathematical background, ideally a knowledge of elementary concepts from measure-theoretic probability, who wish to understand the mathematical models on which the bewildering multitude of current financial instruments used in derivative markets and credit institutions is based. The first edition has been used successfully in a wide range of Master’s programs in mathematical finance and this new edition should prove even more popular in this expanding market. It should equally be useful to risk managers and practitioners looking to master the mathematical tools needed for modern pricing and hedging techniques.
Investments
Stochastic analysis.
Options (Finance)
Securities

Springer finance