Nonparametric Finance

Books

An Introduction to Machine Learning in Finance, With Mathematical Background, Data Visualization, and R

Nonparametric function estimation is an important part of machine learning, which is becoming increasingly important in quantitative finance. Nonparametric Finance provides graduate students and finance professionals with a foundation in nonparametric function

estimation and the underlying mathematics. Combining practical applications, mathematically rigorous presentation, and statistical data analysis into a single volume, this book presents detailed instruction in discrete chapters that allow readers to dip in as needed without reading from beginning to end.

Coverage includes statistical finance, risk management, portfolio management, and securities pricing to provide a practical knowledge base, and the introductory chapter introduces basic finance concepts for readers with a strictly mathematical background. Economic significance

is emphasized over statistical significance throughout, and R code is provided to help readers reproduce the research, computations, and figures being discussed. Strong graphical content clarifies the methods and demonstrates essential visualization techniques, while deep mathematical and statistical insight backs up practical applications.

Written for the leading edge of finance, Nonparametric Finance:

• Introduces basic statistical finance concepts, including univariate and multivariate data analysis, time series analysis, and prediction

• Provides risk management guidance through volatility prediction, quantiles, and value-at-risk

• Examines portfolio theory, performance measurement, Markowitz portfolios, dynamic portfolio selection, and more

• Discusses fundamental theorems of asset pricing, Black-Scholes pricing and hedging, quadratic pricing and hedging, option portfolios, interest rate derivatives, and other asset pricing principles

• Provides supplementary R code and numerous graphics to reinforce complex content

Nonparametric function estimation has received little attention in the context of risk management and option pricing, despite its useful applications and benefits. This book provides the essential background and practical knowledge needed to take full advantage of these little-used methods, and turn them into real-world advantage.

Jussi Klemelä, PhD, is Adjunct Professor at the University of Oulu. His research interests include nonparametric function estimation, density estimation, and data visualization. He is the author of Smoothing of Multivariate Data: Density Estimation and Visualization and Multivariate Nonparametric Regression and Visualization: With R and Applications to Finance.

Preface xxiii

1 Introduction 1

1.1 Statistical Finance 2

1.2 Risk Management 3

1.3 Portfolio Management 5

1.4 Pricing of Securities 6

Part I Statistical Finance 11

2 Financial Instruments 13

2.1 Stocks 13

2.2 Fixed Income Instruments 19

2.3 Derivatives 23

2.4 Data Sets 27

3 Univariate Data Analysis 33

3.1 Univariate Statistics 34

3.2 Univariate Graphical Tools 42

3.3 Univariate ParametricModels 55

3.4 Tail Modeling 61

3.5 Asymptotic Distributions 83

3.6 Univariate Stylized Facts 91

4 Multivariate Data Analysis 95

4.1 Measures of Dependence 95

4.2 Multivariate Graphical Tools 103

4.3 Multivariate ParametricModels 107

4.4 Copulas 111

5 Time Series Analysis 121

5.1 Stationarity and Autocorrelation 122

5.2 Model Free Estimation 128

5.3 Univariate Time Series Models 135

5.4 Multivariate Time Series Models 157

5.5 Time Series Stylized Facts 160

6 Prediction 163

6.1 Methods of Prediction 164

6.2 Forecast Evaluation 170

6.3 Predictive Variables 175

6.4 Asset Return Prediction 182

Part II Risk Management 193

7 Volatility Prediction 195

7.1 Applications of Volatility Prediction 197

7.2 Performance Measures for Volatility Predictors 199

7.3 Conditional Heteroskedasticity Models 200

7.4 Moving Average Methods 205

7.5 State Space Predictors 211

8 Quantiles and Value-at-Risk 219

8.1 Definitions of Quantiles 220

8.2 Applications of Quantiles 223

8.3 Performance Measures for Quantile Estimators 227

8.4 Nonparametric Estimators of Quantiles 233

8.5 Volatility Based Quantile Estimation 240

8.6 Excess Distributions in Quantile Estimation 258

8.7 Extreme ValueTheory in Quantile Estimation 288

8.8 Expected Shortfall 292

Part III Portfolio Management 297

9 Some Basic Concepts of Portfolio Theory 299

9.1 Portfolios and Their Returns 300

9.2 Comparison of Return andWealth Distributions 312

9.3 Multiperiod Portfolio Selection 326

10 Performance Measurement 337

10.1 The Sharpe Ratio 338

10.2 Certainty Equivalent 346

10.3 Drawdown 347

10.4 Alpha and Conditional Alpha 348

10.5 Graphical Tools of Performance Measurement 356

11 Markowitz Portfolios 367

11.1 Variance Penalized Expected Return 369

11.2 Minimizing Variance under a Sufficient Expected Return 372

11.3 Markowitz Bullets 375

11.4 Further Topics in Markowitz Portfolio Selection 381

11.5 Examples of Markowitz Portfolio Selection 383

12 Dynamic Portfolio Selection 385

12.1 Prediction in Dynamic Portfolio Selection 387

12.3 One Risky Asset 394

12.4 Two Risky Assets 405

Part IV Pricing of Securities 419

13 Principles of Asset Pricing 421

13.1 Introduction to Asset Pricing 422

13.2 Fundamental Theorems of Asset Pricing 430

13.3 Evaluation of Pricing and Hedging Methods 456

14 Pricing by Arbitrage 459

14.1 Futures and the Put–Call Parity 460

14.2 Pricing in Binary Models 466

14.3 Black–Scholes Pricing 485

14.4 Black–Scholes Hedging 505

14.5 Black–Scholes Hedging and Volatility Estimation 515

15 Pricing in IncompleteModels 521

15.1 Quadratic Hedging and Pricing 522

15.2 Utility Maximization 523

15.3 Absolutely Continuous Changes of Measures 530

15.4 GARCH Market Models 534

15.5 Nonparametric Pricing Using Historical Simulation 545

15.6 Estimation of the Risk-Neutral Density 551

15.7 Quantile Hedging 555

16.3 Implementations of Local Quadratic Hedging 595

17 Option Strategies 615

17.1 Option Strategies 616

17.2 Profitability of Option Strategies 625

18 Interest Rate Derivatives 649

18.1 Basic Concepts of Interest Rate Derivatives 650

18.2 Interest Rate Forwards 659

18.3 Interest Rate Options 666

18.4 Modeling Interest Rate Markets 669

References 673

Index 681

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