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Introduction to the Economics and Mathematics of Financial Markets : The MIT Press - Jaksa Cvitanic

Introduction to the Economics and Mathematics of Financial Markets

The MIT Press

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"Introduction to the Economics and Mathematics of Financial Markets" fills the longstanding need for an accessible yet serious textbook treatment of financial economics. The book provides a rigorous overview of the subject, while its flexible presentation makes it suitable for use with different levels of undergraduate and graduate students. Each chapter presents mathematical models of financial problems at three different degrees of sophistication: single-period, multi-period, and continuous-time. The single-period and multi-period models require only basic calculus and an introductory probability/statistics course, while an advanced undergraduate course in probability is helpful in understanding the continuous-time models. In this way, the material is given complete coverage at different levels; the less advanced student can stop before the more sophisticated mathematics and still be able to grasp the general principles of financial economics. The book is divided into three parts. The first part provides an introduction to basic securities and financial market organization, the concept of interest rates, the main mathematical models, and quantitative ways to measure risks and rewards. The second part treats option pricing and hedging; here and throughout the book, the authors emphasize the Martingale or probabilistic approach. Finally, the third part examines equilibrium models--a subject often neglected by other texts in financial mathematics, but included here because of the qualitative insight it offers into the behavior of market participants and pricing.

"This book provides a very clear and readable approach to the structure, background, and theory of modern financial markets. It can easily be used as a text for a graduate course in quantitative finance and as a reference by practitioners. Unlike more mathematical treatments, however, most of its content should also be accessible to good MBA students."--Robert J. Elliott, RBC Financial Group Professor of Finance, University of Calgary "This book is the first of its kind--an accessible but rigorous treatment of classic dynamic asset-pricing models, appropriate for master's-level or introductory doctoral courses, and suitable for students from various fields, including economics, finance, or applied mathematics. An excellent contribution." Darrell Duffie, Graduate School of Business, Stanford University "This book is the first of its kind -- an accessible but rigorous treatment of classic dynamic asset-pricing models, appropriate for master's-level or introductory doctoral courses, and suitable for students from various fields, including economics, finance, or applied mathematics. An excellent contribution."--Darrell Duffie, Graduate School of Business, Stanford University

Prefacep. xvii
The Setting: Markets, Models, Interest Rates, Utility Maximization, Riskp. 1
Financial Marketsp. 3
Bondsp. 3
Stocksp. 7
Derivativesp. 9
Organization of Financial Marketsp. 20
Marginsp. 22
Transaction Costsp. 24
Summaryp. 25
Problemsp. 26
Further Readingsp. 29
Interest Ratesp. 31
Computation of Interest Ratesp. 31
Present Valuep. 35
Term Structure of Interest Rates and Forward Ratesp. 41
Summaryp. 48
Problemsp. 49
Further Readingsp. 51
Models of Securities Prices in Financial Marketsp. 53
Single-Period Modelsp. 54
Multiperiod Modelsp. 58
Continuous-Time Modelsp. 62
Modeling Interest Ratesp. 79
Nominal Rates and Real Ratesp. 81
Arbitrage and Market Completenessp. 83
Appendixp. 94
Summaryp. 97
Problemsp. 98
Further Readingsp. 101
Optimal Consumption/Portfolio Strategiesp. 103
Preference Relations and Utility Functionsp. 103
Discrete-Time Utility Maximizationp. 113
Utility Maximization in Continuous Timep. 122
Duality/Martingale Approach to Utility Maximizationp. 128
Transaction Costsp. 138
Incomplete and Asymmetric Informationp. 139
Appendix: Proof of Dynamic Programming Principlep. 145
Summaryp. 146
Problemsp. 147
Further Readingsp. 150
Riskp. 153
Risk versus Return: Mean-Variance Analysisp. 153
VaR: Value at Riskp. 167
Summaryp. 172
Problemsp. 172
Further Readingsp. 175
Pricing and Hedging of Derivative Securitiesp. 177
Arbitrage and Risk-Neutral Pricingp. 179
Arbitrage Relationships for Call and Put Options; Put-Call Parityp. 179
Arbitrage Pricing of Forwards and Futuresp. 184
Risk-Neutral Pricingp. 188
Appendixp. 206
Summaryp. 211
Problemsp. 213
Further Readingsp. 215
Option Pricingp. 217
Option Pricing in the Binomial Modelp. 217
Option Pricing in the Merton-Black-Scholes Modelp. 222
Pricing American Optionsp. 228
Options on Dividend-Paying Securitiesp. 235
Other Types of Optionsp. 240
Pricing in the Presence of Several Random Variablesp. 247
Merton's Jump-Diffusion Model*p. 260
Estimation of Variance and ARCH/GARCH Modelsp. 262
Appendix: Derivation of the Black-Scholes Formulap. 265
Summaryp. 267
Problemsp. 268
Further Readingsp. 273
Fixed-Income Market Models and Derivativesp. 275
Discrete-Time Interest-Rate Modelingp. 275
Interest-Rate Models in Continuous Timep. 286
Swaps, Caps, and Floorsp. 301
Credit/Default Riskp. 306
Summaryp. 308
Problemsp. 309
Further Readingsp. 312
Hedgingp. 313
Hedging with Futuresp. 313
Portfolios of Options as Trading Strategiesp. 317
Hedging Options Positions; Delta Hedgingp. 322
Perfect Hedging in a Multivariable Continuous-Time Modelp. 334
Hedging in Incomplete Marketsp. 335
Summaryp. 336
Problemsp. 337
Further Readingsp. 340
Bond Hedgingp. 341
Durationp. 341
Immunizationp. 347
Convexityp. 351
Summaryp. 352
Problemsp. 352
Further Readingsp. 353
Numerical Methodsp. 355
Binomial Tree Methodsp. 355
Monte Carlo Simulationp. 361
Numerical Solutions of PDEs; Finite-Difference Methodsp. 373
Summaryp. 377
Problemsp. 378
Further Readingsp. 380
Equilibrium Modelsp. 381
Equilibrium Fundamentalsp. 383
Concept of Equilibriump. 383
Single-Agent and Multiagent Equilibriump. 389
Pure Exchange Equilibriump. 391
Existence of Equilibriump. 398
Summaryp. 406
Problemsp. 406
Further Readingsp. 407
CAPMp. 409
Basic CAPMp. 409
Economic Interpretationsp. 413
Alternative Derivation of the CAPM*p. 420
Continuous-Time, Intertemporal CAPM*p. 423
Consumption CAPM*p. 427
Summaryp. 430
Problemsp. 430
Further Readingsp. 432
Multifactor Modelsp. 433
Discrete-Time Multifactor Modelsp. 433
Arbitrage Pricing Theory (APT)p. 436
Multifactor Models in Continuous Time*p. 438
Summaryp. 445
Problemsp. 445
Further Readingsp. 445
Other Pure Exchange Equilibriap. 447
Term-Structure Equilibriap. 447
Informational Equilibriap. 451
Equilibrium with Heterogeneous Agentsp. 457
International Equilibrium; Equilibrium with Two Pricesp. 461
Summaryp. 466
Problemsp. 466
Further Readingsp. 467
Appendix: Probability Theory Essentialsp. 469
Discrete Random Variablesp. 469
Continuous Random Variablesp. 470
Several Random Variablesp. 471
Normal Random Variablesp. 472
Properties of Conditional Expectationsp. 474
Martingale Definitionp. 476
Random Walk and Brownian Motionp. 476
Referencesp. 479
Indexp. 487
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780262033206
ISBN-10: 0262033208
Series: The MIT Press
Audience: Professional
For Ages: 18+ years old
Format: Hardcover
Language: English
Number Of Pages: 516
Published: 26th March 2004
Country of Publication: US
Dimensions (cm): 22.9 x 17.8  x 2.9
Weight (kg): 0.93