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Finance, Economics, and Mathematics



"For more than four decades, Vasicek has pioneered important research about the term structure of interest rates, credit analysis, bond portfolio management, and general equilibrium theory. He has always brought just the right mathematical tools to solve every problem he has tackled. This historical compendium of his work still sparkles with creativity."
—Richard Roll, Professor Emeritus, UCLA Anderson School of Management

"Oldrich Vasicek has had an exemplary, inspiring, and enviable career in finance. From his prescient 1977 paper on term structure to his model of credit valuation, he has persistently shown us how to combine rigorous science with economics and intuition to provide remarkable insight into business. This wonderful collection of his papers reflects the high scientific standards he has brought to bear on the field."
—Emanuel Derman, Director of the MS Program in Financial Engineering, Columbia University


Finance, Economics, and Mathematics is the complete Vasicek reference work, including published and unpublished work and interviews with the man himself. The name Oldrich Vasicek is synonymous with cutting-edge research in finance, and this book comes straight from the source to bring you the groundbreaking papers from one of the founders of the field. From his early work in yield curve dynamics, to the mean-reverting short-rate model, to his thoughts on derivatives pricing, to his work on credit risk, to his most recent research on the economics of interest rates, this book represents a compilation of an industry leader's life's work. If you're involved in finance today, you apply his theory in fundamental practice every day; this book puts his work all in a single volume you'll turn to again and again.

  • Explore Vasicek's insights on the foundational topics he helped create
  • Discover the research and ideas that have gone unpublished—until now
  • Understand yield curves and the Vasicek model from the source himself
  • Follow the ideas that revolutionized portfolio credit risk measurement

Finance, Economics, and Mathematics is the definitive Vasicek reference every finance professional needs.

OLDRICH ALFONS VASICEK works in mathematical finance, particularly on the development of quantitative models of firms, financial instruments, and financial markets. He was a founding partner of KMV Corporation, a firm pioneering the use of structural models for credit valuation. He is an inductee into the Derivatives Strategy Hall of Fame, the Fixed Income Analysts Society Hall of Fame, and the Risk Magazine Hall of Fame.

Foreword (by Robert C. Merton) ix

Preface xi

PART ONE Efforts and Opinions 1

CHAPTER 1 Introduction to Part I 3

CHAPTER 2 Lifetime Achievement Award (by Dwight Cass) 7

CHAPTER 3 One-on-One Interview with Oldrich Alfons Vasicek (by Nina Mehta) 13

CHAPTER 4 Credit Superquant (by Robert Hunter) 21

PART TWO Term Structure of Interest Rates 27

CHAPTER 5 Introduction to Part II 29

CHAPTER 6 An Equilibrium Characterization of the Term Structure 33

CHAPTER 7 The Liquidity Premium 45

CHAPTER 8 Term Structure Modeling Using Exponential Splines (with Gifford Fong) 49

CHAPTER 9 The Heath, Jarrow, Morton Model 63

PART THREE General Equilibrium 65

CHAPTER 10 Introduction to Part III 67

CHAPTER 11 The Economics of Interest Rates 71

CHAPTER 12 General Equilibrium with Heterogeneous Participants and Discrete Consumption Times 89

CHAPTER 13 Independence of Production and Technology Risks 107

CHAPTER 14 Risk-Neutral Economy and Zero Price of Risk 111

PART FOUR Credit 125

CHAPTER 15 Introduction to Part IV 127

CHAPTER 16 Credit Valuation 131

CHAPTER 17 Probability of Loss on Loan Portfolio 143

CHAPTER 18 Limiting Loan Loss Probability Distribution 147

CHAPTER 19 Loan Portfolio Value 149

CHAPTER 20 The Empirical Test of the Distribution of Loan Portfolio Losses 161

PART FIVE Markets, Portfolios, and Securities 163

CHAPTER 21 Introduction to Part V 165

CHAPTER 22 The Efficient Market Model (with John A. McQuown) 169

CHAPTER 23 A Risk Minimizing Strategy for Portfolio Immunization (with Gifford Fong) 195

CHAPTER 24 The Tradeoff between Return and Risk in Immunized Portfolios (with Gifford Fong) 203

CHAPTER 25 Bond Performance: Analyzing Sources of Return (with Gifford Fong and Charles J. Pearson) 213

CHAPTER 26 The Best-Return Strategy 223

CHAPTER 27 Volatility: Omission Impossible (with Gifford Fong and Daihyun Yoo) 237

CHAPTER 28 A Multidimensional Framework for Risk Analysis (with Gifford Fong) 247

CHAPTER 29 Plugging into Electricity (with Hélyette Geman) 261

CHAPTER 30 Pricing of Energy Derivatives 277

PART SIX Probability Theory and Statistics 281

CHAPTER 31 Introduction to Part VI 283

CHAPTER 32 A Note on Using Cross-sectional Information in Bayesian Estimation of Security Betas 287

CHAPTER 33 A Series Expansion for the Bivariate Normal Integral 297

CHAPTER 34 A Conditional Law of Large Numbers 305

CHAPTER 35 A Test for Normality Based on Sample Entropy 315

CHAPTER 36 Monotone Measures of Ergodicity for Markov Chains (with Julian Keilson) 325

CHAPTER 37 An Inequality for the Variance of Waiting Time under a General Queueing Discipline 333

About the Author 339

Index 341