Introduction to the Mathematics of Financial Derivatives

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.
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Book details

List price: $107.00
Edition: 2nd
Copyright year: 2000
Publisher: Elsevier Science & Technology Books
Publication date: 5/19/2000
Binding: Hardcover
Pages: 527
Size: 6.50" wide x 9.50" long x 1.25" 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
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