Introduction to the Mathematics of Financial Derivatives

Name: Introduction to the Mathematics of Financial Derivatives
Price: 16.42 USD
Availability: InStock
ISBN: 9780125153928

ISBN-10: 0125153929

ISBN-13: 9780125153928

Edition: 2nd 2000 (Revised)

Authors: Salih N. Neftci

List price: $107.00

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Description:

Offering a step-by-step explanation of the mathematical models used to price derivatives, this second edition has one expanded chapter, six new ones, and chapter-concluding exercises. The reader does not to have a thorough mathematical background.

Book details

List price: $107.00
Edition: 2nd
Copyright year: 2000
Publisher: Elsevier Science & Technology
Publication date: 6/22/2000
Binding: Hardcover
Pages: 527
Size: 5.98" wide x 9.02" long x 0.46" tall
Weight: 1.936
Language: English



Preface to the Second Edition


Introduction



Financial Derivatives: A Brief Introduction



Introduction



Definitions



Types of Derivatives



Forwards and Futures



Options



Swaps



Conclusions



References



Exercises



A Primer on the Arbitrage Theorem



Introduction



Notation



A Basic Example of Asset Pricing



A Numerical Example



An Application: Lattice Models



Payouts and Foreign Currencies



Some Generalizations



Conclusions: A Methodology for Pricing Assets



References



Appendix: Generalization of the Arbitrage Theorem



Exercises



Calculus in Deterministic and Stochastic Environments



Introduction



Some Tools of Standard Calculus



Functions



Convergence and Limit



Partial Derivatives



Conclusions



References



Exercises



Pricing Derivatives: Models and Notation



Introduction



Pricing Functions



Application: Another Pricing Method



The Problem



References



Exercises



Tools in Probability Theory



Introduction



Probability



Moments



Conditional Expectations



Some Important Models



Markov Processes and Their Relevance



Convergence of Random Variables



Conclusions



References



Exercises



Martingales and Martingale Representations



Introduction



Definitions



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



Conclusions



References



Exercises



Differentiation in Stochastic Environments



Introduction



Motivation



A Framework for Discussing Differentiation



The "Size" of Incremental Errors



One Implication



Putting the Results Together



Conclusions



References



Exercises



The Wiener Process and Rare Events in Financial Markets



Introduction



Two Generic Models



SDE in Discrete Intervals, Again



Characterizing Rare and Normal Events



A Model for Rare Events



Moments That Matter



Conclusions



Rare and Normal Events in Practice



References



Exercises



Integration in Stochastic Environments: The Ito Integral



Introduction



The Ito Integral



Properties of the Ito Integral



Other Properties of the Ito Integral



Integrals with Respect to Jump Processes



Conclusions



References



Exercises



Ito's Lemma



Introduction



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



Conclusions



References



Exercises



The Dynamics of Derivative Prices: Stochastic Differential Equations



Introduction



A Geometric Description of Paths Implied by SDEs



Solution of SDEs



Major Models of SDEs



Stochastic Volatility



Conclusions



References



Exercises



Pricing Derivative Products: Partial Differential Equations



Introduction



Forming Risk-Free Portfolios



Accuracy of the Method



Partial Differential Equations



Classification of PDEs



A Reminder: Bivariate, Second-Degree Equations



Types of PDEs



Conclusions



References



Exercises



The Black--Scholes PDE: An Application



Introduction



The Black--Scholes PDE



PDEs in Asset Pricing



Exotic Options



Solving PDEs in Practice



Conclusions



References



Exercises



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



Conclusions



References



Exercises



Equivalent Martingale Measures: Applications



Introduction



A Martingale Measure



Converting Asset Prices into Martingales



Application: The Black--Scholes Formula



Comparing Martingale and PDE Approaches



Conclusions



References



Exercises



New Results and Tools for Interest-Sensitive Securities



Introduction



A Summary



Interest Rate Derivatives



Complications



Conclusions



References



Exercises



Arbitrage Theorem in a New Setting: Normalization and Random Interest Rates



Introduction



A Model for New Instruments



Conclusions



References



Exercises



Modeling Term Structure and Related Concepts



Introduction



Main Concepts



A Bond Pricing Equation



Forward Rates and Bond Prices



Conclusions: Relevance of the Relationships



References



Exercises



Classical and HJM Approaches to Fixed Income



Introduction



The Classical Approach



The HJM Approach to Term Structure



How to Fit r[subscript t] to Initial Term Structure



Conclusions



References



Exercises



Classical PDE Analysis for Interest Rate Derivatives



Introduction



The Framework



Market Price of Interest Rate Risk



Derivation of the PDE



Closed-Form Solutions of the PDE



Conclusions



References



Exercises



Relating Conditional Expectations to PDEs



Introduction



From Conditional Expectations to PDEs