Mathematical Techniques in Finance : Tools

Originally published in 2003,Mathematical Techniques in Financehas become a standard textbook for master's-level finance courses containing a significant quantitative element while also being suitable for finance PhD students. This fully revised second edition continues to offer a carefully crafted blend of numerical applications and theoretical grounding in economics, finance, and mathematics, and provides plenty of opportunities for students to practice applied mathematics and cutting-edge finance. Ales Cernyacute; mixes tools from calculus, linear algebra, probability theory, numerical mathematics, and programming to analyze in an accessible way some of the most intriguing problems in financial economics. The textbook is the perfect hands-on introduction to asset pricing, optimal portfolio selection, risk measurement, and investment evaluation.The new edition includes the most recent research in the area of incomplete markets and unhedgeable risks, adds a chapter on finite difference methods, and thoroughly updates all bibliographic references. Eighty figures, over seventy examples, twenty-five simple ready-to-run computer programs, and several spreadsheets enhance the learning experience. All computer codes have been rewritten using MATLAB and online supplementary materials have been completely updated. A standard textbook for graduate finance courses Introduction to asset pricing, portfolio selection, risk measurement, and investment evaluation Detailed examples and MATLAB codes integrated throughout the text Exercises and summaries of main points conclude each chapter

Preface to the Second Edition	p. xiii
From the Preface to the First Edition	p. xix
The Simplest Model of Financial Markets	p. 1
One-Period Finite State Model	p. 1
Securities and Their Payoffs	p. 3
Securities as Vectors	p. 3
Operations on Securities	p. 4
The Matrix as a Collection of Securities	p. 6
Transposition	p. 6
Matrix Multiplication and Portfolios	p. 8
Systems of Equations and Hedging	p. 10
Linear Independence and Redundant Securities	p. 12
The Structure of the Marketed Subspace	p. 14
The Identity Matrix and Arrow-Debreu Securities	p. 16
Matrix Inverse	p. 17
Inverse Matrix and Replicating Portfolios	p. 17
Complete Market Hedging Formula	p. 19
Summary	p. 20
Notes	p. 21
Exercises	p. 22
Arbitrage and Pricing in the One-Period Model	p. 25
Hedging with Redundant Securities and Incomplete Market	p. 25
Finding the Best Approximate Hedge	p. 29
Minimizing the Expected Squared Replication Error	p. 32
Numerical Stability of Least Squares	p. 34
Asset Prices, Returns and Portfolio Units	p. 36
Arbitrage	p. 38
No-Arbitrage Pricing	p. 40
State Prices and the Arbitrage Theorem	p. 41
State Prices and Asset Returns	p. 44
Risk-Neutral Probabilities	p. 45
State Prices and No-Arbitrage Pricing	p. 46
Asset Pricing Duality	p. 47
Summary	p. 48
Notes	p. 49
Appendix: Least Squares with QR Decomposition	p. 49
Exercises	p. 52
Risk and Return in the One-Period Model	p. 55
Utility Functions	p. 56
Expected Utility Maximization	p. 59
The Existence of Optimal Portfolios	p. 61
Reporting Expected Utility in Terms of Money	p. 62
Normalized Utility and Investment Potential	p. 63
Quadratic Utility	p. 67
The Sharpe Ratio	p. 69
Arbitrage-Adjusted Sharpe Ratio	p. 71
The Importance of Arbitrage Adjustment	p. 75
Portfolio Choice with Near-Arbitrage Opportunities	p. 77
Summary	p. 79
Notes	p. 81
Exercises	p. 82
Numerical Techniques for Optimal Portfolio Selection in Incomplete Markets	p. 84
Sensitivity Analysis of Portfolio Decisions with the CRRA Utility	p. 84
Newton's Algorithm for Optimal Investment with CRRA Utility	p. 88
Optimal CRRA Investment Using Empirical Return Distribution	p. 90
HARA Portfolio Optimizer	p. 94
HARA Portfolio Optimization with Several Risky Assets	p. 96
Quadratic Utility Maximization with Multiple Assets	p. 99
Summary	p. 102
Notes	p. 102
Exercises	p. 102
Pricing in Dynamically Complete Markets	p. 104
Options and Portfolio Insurance	p. 104
Option Pricing	p. 105
Dynamic Replicating Trading Strategy	p. 108
Risk-Neutral Probabilities in a Multi-Period Model	p. 116
The Law of Iterated Expectations	p. 119
Summary	p. 121
Notes	p. 121
Exercises	p. 121
Towards Continuous Time	p. 125
IID Returns, and the Term Structure of Volatility	p. 125
Towards Brownian Motion	p. 127
Towards a Poisson Jump Process	p. 136
Central Limit Theorem and Infinitely Divisible Distributions	p. 142
Summary	p. 143
Notes	p. 145
Exercises	p. 145
Fast Fourier Transform	p. 147
Introduction to Complex Numbers and the Fourier Transform	p. 147
Discrete Fourier Transform (DFT)	p. 152
Fourier Transforms in Finance	p. 153
Fast Pricing via the Fast Fourier Transform (FFT)	p. 158
Further Applications of FFTs in Finance	p. 162
Notes	p. 166
Appendix	p. 167
Exercises	p. 169
Information Management	p. 170
Information: Too Much of a Good Thing?	p. 170
Model-Independent Properties of Conditional Expectation	p. 174
Summary	p. 178
Notes	p. 179
Appendix: Probability Space	p. 179
Exercises	p. 183
Martingales and Change of Measure in Finance	p. 187
Discounted Asset Prices Are Martingales	p. 187
Dynamic Arbitrage Theorem	p. 192
Change of Measure	p. 193
Dynamic Optimal Portfolio Selection in a Complete Market	p. 198
Summary	p. 206
Notes	p. 208
Exercises	p. 208
Brownian Motion and Itï¿½o Formulae	p. 213
Continuous-Time Brownian Motion	p. 213
Stochastic Integration and Itï¿½o Processes	p. 218
Important Itï¿½o Processes	p. 220
Notes	p. 230
Exercises	p. 23
Table of Contents provided by Publisher. All Rights Reserved.

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Mathematical Techniques in Finance : Tools for Incomplete Markets (Second Edition)

Summary

Table of Contents

Supplemental Materials