Includes bibliographical references (p. 509-511) and index.

Types of Derivatives -- Forwards and Futures -- Options -- Swaps -- A Primer on the Arbitrage Theorem -- A Basic Example of Asset Pricing -- A Numerical Example -- An Application: Lattice Models -- Payouts and Foreign Currencies -- Conclusions: A Methodology for Pricing Assets -- Appendix: Generalization of the Arbitrage Theorem -- Calculus in Deterministic and Stochastic Environments -- Some Tools of Standard Calculus -- Functions -- Convergence and Limit -- Partial Derivatives -- Pricing Derivatives: Models and Notation -- Pricing Functions -- Application: Another Pricing Method -- The Problem -- Tools in Probability Theory -- Probability -- Moments -- Conditional Expectations -- Some Important Models -- Markov Processes and Their Relevance -- Convergence of Random Variables -- Martingales and Martingale Representations -- The Use of Martingales in Asset Pricing -- Relevance of Martingales in Stochastic Modeling -- Properties of Martingale Trajectories -- Examples of Martingales -- The Simplest Martingale -- Martingale Representations -- The First Stochastic Integral -- Martingale Methods and Pricing -- A Pricing Methodology -- Differentiation in Stochastic Environments -- Motivation -- A Framework for Discussing Differentiation -- The "Size" of Incremental Errors -- One Implication -- Putting the Results Together -- The Wiener Process and Rare Events in Financial Markets -- Two Generic Models -- SDE in Discrete Intervals, Again -- Characterizing Rare and Normal Events -- A Model for Rare Events -- Moments That Matter -- Rare and Normal Events in Practice -- Integration in Stochastic Environments: The Ito Integral -- The Ito Integral -- Properties of the Ito Integral -- Other Properties of the Ito Integral -- Integrals with Respect to Jump Processes -- Ito's Lemma -- Types of Derivatives -- Ito's Lemma -- The Ito Formula -- Uses of Ito's Lemma -- Integral Form of Ito's Lemma -- Ito's Formula in More Complex Settings -- The Dynamics of Derivative Prices: Stochastic Differential Equations -- A Geometric Description of Paths Implied by SDEs -- Solution of SDEs -- Major Models of SDEs -- Stochastic Volatility -- Pricing Derivative Products: Partial Differential Equations -- Forming Risk-Free Portfolios -- Accuracy of the Method -- Partial Differential Equations -- Classification of PDEs -- A Reminder: Bivariate, Second-Degree Equations -- Types of PDEs -- The Black--Scholes PDE: An Application -- The Black--Scholes PDE -- PDEs in Asset Pricing -- Exotic Options -- Solving PDEs in Practice -- Pricing Derivative Products: Equivalent Martingale Measures -- Translations of Probabilities -- Changing Means -- The Girsanov Theorem -- Statement of the Girsanov Theorem -- A Discussion of the Girsanov Theorem -- Which Probabilities? -- A Method for Generating Equivalent Probabilities -- Equivalent Martingale Measures: Applications -- A Martingale Measure -- Converting Asset Prices into Martingales -- Application: The Black--Scholes Formula -- Comparing Martingale and PDE Approaches -- New Results and Tools for Interest-Sensitive Securities -- Interest Rate Derivatives -- Complications -- Arbitrage Theorem in a New Setting: Normalization and Random Interest Rates -- A Model for New Instruments -- Modeling Term Structure and Related Concepts -- Main Concepts -- A Bond Pricing Equation -- Forward Rates and Bond Prices -- Conclusions: Relevance of the Relationships -- Classical and HJM Approaches to Fixed Income -- The Classical Approach -- The HJM Approach to Term Structure -- How to Fit r[subscript t] to Initial Term Structure -- Classical PDE Analysis for Interest Rate Derivatives -- The Framework -- Market Price of Interest Rate Risk -- Derivation of the PDE -- Closed-Form Solutions of the PDE -- Relating Conditional Expectations to PDEs -- From Conditional Expectations to PDEs.

This popular text, publishing Summer 1999 in its Second Edition, introduces the mathematics underlying the pricing of derivatives. The increase of interest in dynamic pricing models stems from their applicability to practical situations: with the freeing of exchange, interest rates, and capital controls, the markets for derivative products has matured and pricing models have become more accurate. Professor Neftci's book answers the need for a resource targeting professionals, Ph.D. students, and advanced MBA students who are specifically interested in these financial products. The Second Edition is designed to make the book the main text in first year masters and Ph.D. programs for certain courses, and will continue to be an important manual for market professionals.