Simulation and Optimization in Finance
Simulation and Optimization in Finance
Simulation and Optimization in Finance The Frank j. Fabozzi series Fixed Income Securities, Second edition by frank J Fabozzi Focus on Value: A Corporate and Investor Guide to Wealth Creation by James L. Grant and James A. Abate Handbook of Global Fixed Income Calculations by Dragomir Krgin Managing a Corporate Bond portfolio by Leland E. Crabbe and Frank J Fabozzi Real options and Option-Embedded Securities by William T. Moore Capital Budgeting: Theory and Practice by Pamela P. Peterson and Frank J. Fabozzi The Exchange-Traded Funds Manual by Gary L. Gastineau Professional perspectives on Fixed Income Portfolio Management, Volume 3 edited by Frank J Fabozzi Investing in Emerging Fixed Income Markets edited by Frank J. Fabozzi and Efstathia Pilarinu Handbook of alternative Assets by Mark J. P.Anson The Global Money Markets by Frank J Fabozzi, Steven V Mann, and Moorad Choudhry The handbook of financial Instruments edited by Frank J Fabozzi Interest Rate, Term Structure, and Valuation Modeling edited by Frank J. Fabozzi Investment Performance Measurement by bruce J Feibel The Handbook of equity Style management edited by T. Daniel Coggin and Frank J. Fabozzi The Theory and Practice of Investment Management edited by Frank J Fabozzi and Harry M. Markowitz Foundations of Economic Value Added, Second Edition by James L.Grant Financial management and Analysis, Second Edition by Frank J. Fabozzi and Pamela P. Peterson Measuring and Controlling Interest Rate and Credit Risk, Second Edition by Frank J Fabozzi, Steven V. Mann, and Moorad Choudhry Professional Perspectives on Fixed Income Portfolio Management, Volume 4 edited by Frank J Fabozzi he Handbook of european Fixed Income Securities edited by Frank J Fabozzi and Moorad Choudhry The Handbook of european Structured Financial Products edited by Frank J. Fabozzi and Moorad Choudhry The Mathematics of financial Modeling and Investment Management by Sergio M. Focardi and Frank J Fabozzi Short Selling: Strategies, Risks, and Rewards edited by Frank J. Fabozzi The Real estate Investment Handbook by G. Timothy Haight and Daniel Singer Market Neutral Strategies edited by Bruce I Jacobs and Kenneth N. Levy Securities fi Securities Lending and Repurchase agreements edited by Frank J. Fabozzi and Steven V. Mann Fat-Tailed and Skewed Asset Return Distributions by Svetlozar T. Rachev, Christian Menn, and Frank J. Fabozz Financial modeling of the equity Market: From CAPM to Cointegration by Frank J. Fabozzi, Sergio M. Focardi, and Petter n. Kolm Advanced Bond portfolio Management: Best Practices in Modeling and Strategies edited by Frank J Fabozzi, Lionel Martellini, and Philippe Priaulet Analysis of financial Statements, Second Edition by Pamela P. Peterson and Frank J. Fabozzi Collateralized Debt Obligations: Structures and Analysis, Second Edition by Douglas J. Lucas, Laurie S. Goodman, and Frank J. fabozzi Handbook of Alternative Assets, Second Edition by Mark J. P. Anson Introduction to Structured Finance by Frank J. Fabozzi, Henry A. Davis, and Moorad Choudhry Financial econometrics by svetlozar achev, Stefan Mittnik, Frank J. Fabozzi, Sergio M. Focardi, and Teo Jasic Developments in Collateralized debt obligations: New Products and Insights by Douglas J. Lucas, Laurie S. Goodman, Frank J Fabozzi, and Rebecca J. manning Robust portfolio Optimization and Management by Frank J Fabozzi, Peter N. Kolm, Dessislava A. Pachamanova, and ergo ocar Advanced Stochastic Models, Risk Assessment, and Portfolio Optimizations by Svetlozar T Rachev, Stogan V. Stoyanov, and Frank J. Fabozzi How to Select Investment Managers and Evaluate Performance by G. Timothy Haight, Stephen O. Morrell, and Glenn e. ross Bayesian Methods in Finance by Svetlozar T Rachev, John S J. Hsu, Biliana S. Bagasheva, and frank J. Fabozzi The Handbook of commodity Investing by Frank J Fabozzi, Roland Fuss, and Dieter G. Kaiser The Handbook of municipal Bonds edited by Sylvan G. Feldstein and Frank J. Fabozzi Subprime Mortgage Credit Derivatives by Laurie S Goodman, Shumin Li, Douglas J. Lucas, Thomas A Zimmerman, and Frank J. fabozzi Introduction to Securitization by frank Fabozzi and vinod Kothari Structured products and related Credit derivatives edited by brian P Lancaster, Glenn M. Schultz, and frank J. Fabozzi Handbook of Finance: Volume I: Financial Markets and Instruments edited by Frank J Fabozzi Handbook of finance: Volume II: Financial Management and Asset Management edited by Frank J. Fabozzi Handbook of finance: Volume Ill: Valuation, Financial Modeling, and Quantitative Tools edited by Frank J Fabozzi Finance: Capital Markets, Financial Management, and Investment Management by Frank J Fabozzi and Pamela Peterson-Drake Active Private equity real estate Strategy edited by David J. Lynn Foundations and Applications of the Time value of money by Pamela Peterson-Drake and Frank J Fabozzi Leveraged Finance: Concepts, Methods, and Trading of High-Yield Bonds, Loans, and Derivatives by Stephen Antczal Douglas Lucas, and Frank J Fabozzi Modern Financial Systems: Theory and Applications by Edwin Neave Institutional Investment Management: Equity and Bond Portfolio Strategies and Applications by Frank J. Fabozzi Quantitative Equity Investing: Techniques and Strategies by Frank J. Fabozzi, Sergio M. Focardi, Petter N. Kolm Simulation and Optimization in Finance: Modeling with MATLAB, @RISK, or VBa by Dessislava A Pachamanova and Frank j. Fabozzi Simulation and Optimization in Finance Modeling with MATLAB @RⅠSK, or vba DESSISLAVA A. PACHAMANOVA FRANK J FABOZZI WILEY John Wiley sons, Inc. Copyright o 2010 by John Wiley Sons, Inc. All rights reserved Published by john Wiley sons, Inc, Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization througl payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc, 222 Rosewood Drive, Danvers, MA 01923, (978)750-8400, fax (978)646-8600, or on the Web atwww.copyright.comRequeststothePublisherforpermissionshouldbeaddressedtothe Permissions Department, John Wiley Sons, Inc, 111 River Street, Hoboken, NJ07030 201)748-6011,fax(201)748-6008,oronlineathttp://www.wiley.com/go/permissions Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created r extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services or for technical support please contact our Customer Care Department within the United States at(800)762-2974, outside the United States at (317)572-3993 or fax (317)572-4002 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visitourWebsiteatwww.wiley.com Library of congress Cataloging-in-Publication data Pachamanova. dessislava a a Simulation and optimization in finance modeling with MaTlaB, @RiSK, or VBA/ essislava A Pachamanova, Frank j. Fabozzi p. cm-(Frank J Fabozzi series; 173) Includes index ISBN978-0-470-37189-3( cloth);978-0-470-88211-5(ebk); 978-0-470-88212-2(ebk) 1. Finance-Mathematical models-Computer programs. I Fabozzi, Frank J. Il. title HG106.P332010 332.0285′53-dc22 2010027038 Printed in the United States of america 10987654321 Dessislava a. pachamanova To my husband, Christian, and my children, Anna and coleman Frank j. fabozzi To my wife, Donna, and my children, Patricia, Karly, and francesco Contents Preface About the authons X Acknowledgments XVII CHAPTER 1 Introduction Optimization; Simulation: Outline of topics PART ONE Fundamental concepts CHAPTER 2 Important Finance Concepts Basic Theory of Interest; Asset Classes; Basic Trading Terminology; Calculating Rate of Return; Valuation; Important Concepts in Fixed Income; Summary; Notes CHAPTER 3 Random variables, probability Distributions, and Important Statistical Concepts What is a Probability Distribution? Bernoulli Probability distribution and Probability mass Functions: binomial Probability Distribution and Discrete distributions: normal distribution and Probability density Functions; Concept of cumulative Probability; Describing Distributions; Brief Overview of some important probability distributions Dependence between Two Random Variables Covariance and correlation: Sums of random Variables; joint Probability Distributions and Conditional Probability; From Probability theory to Statistical Measurement: Probability Distributions and Sampling; Summary; Software Hints; Notes CONTENTS CHAPTER 4 Simulation Modeling Monte Carlo Simulation: A Simple Example; Why Use Simulation? Important Questions in Simulation Modeling; Random Number Generation; Summary; Software Hints: notes CHAPTER 5 Optimization Modeling Optimization Formulations; Important Types of Optimization Problems; Optimization Problem Formulation Examples; Optimization Algorithms Optimization duality; multistage Optimization Optimization Software; Summary; Software Hints; Notes CHAPTER 6 Optimization under Uncertainty 211 Dynamic Programming; Stochastic Programming Robust Optimization; Summary; Notes PART TWO Portfolio Optimization and Risk Measures CHAPTER Z Asset diversification and efficient frontiers 245 The Case for Diversification: The Classical Mean-Variance Optimization Framework; Efficient Frontiers: Alternative Formulations of the classical Mean-Variance Optimization Problem; The Capital Market Line; Expected Utility Theory; Summary; Software hints: notes CHAPTER 8 Advances in the theory of portfolio Risk Measures 277 Value-At-Risk and the Concept of Coherent risk Onal Classes of risk measures: value-At-Risk: conditi Measures; Summary; Software Hints; Notes CHAPTER 9 Equity portfolio selection in Practice The Investment Process: Portfolio constraints Commonly Used in Practice; Benchmark Exposure and Tracking Error Minimization; Incorporating
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