You have no items in your shopping cart.

A Workout in Computational Finance

A Workout in Computational Finance

  • Author:
  • Publisher: John Wiley & Sons
  • ISBN: 9781119971917
  • Published In: August 2013
  • Format: Hardback , 336 pages
  • Jurisdiction: International ? Disclaimer:
    Countri(es) stated herein are used as reference only

List Price: HKD 950.00

HKD 921.50 Save HKD 28.50 (3%)

Delivery Time: around 1-2 weeks
Extra 2-10 working days if shipping address outside Hong Kong
Free delivery Hong Kong?
Hong Kong: free delivery (order over HKD 1000)
OR
  • Description 
  • Contents 
  • Author 
  • Details

    A comprehensive introduction to various numerical methods used in computational finance today

    Quantitative skills are a prerequisite for anyone working in finance or beginning a career in the field, as well as risk managers. A thorough grounding in numerical methods is necessary, as is the ability to assess their quality, advantages, and limitations. This book offers a thorough introduction to each method, revealing the numerical traps that practitioners frequently fall into. Each method is referenced with practical, real-world examples in the areas of valuation, risk analysis, and calibration of specific financial instruments and models. It features a strong emphasis on robust schemes for the numerical treatment of problems within computational finance. Methods covered include PDE/PIDE using finite differences or finite elements, fast and stable solvers for sparse grid systems, stabilization and regularization techniques for inverse problems resulting from the calibration of financial models to market data, Monte Carlo and Quasi Monte Carlo techniques for simulating high dimensional systems, and local and global optimization tools to solve the minimization problem.

  • Acknowledgements xiii

    About the Authors xv

    1 Introduction and Reading Guide 1

    2 Binomial Trees 7

    2.1 Equities and Basic Options 7

    2.2 The One Period Model 8

    2.3 The Multiperiod Binomial Model 9

    2.4 Black-Scholes and Trees 10

    2.5 Strengths and Weaknesses of Binomial Trees 12

    2.6 Conclusion 16

    3 Finite Differences and the Black-Scholes PDE 17

    3.1 A Continuous Time Model for Equity Prices 17

    3.2 Black-Scholes Model: From the SDE to the PDE 19

    3.3 Finite Differences 23

    3.4 Time Discretization 27

    3.5 Stability Considerations 30

    3.6 Finite Differences and the Heat Equation 30

    3.7 Appendix: Error Analysis 36

    4 Mean Reversion and Trinomial Trees 39

    4.1 Some Fixed Income Terms 39

    4.2 Black76 for Caps and Swaptions 43

    4.3 One-Factor Short Rate Models 45

    4.3.1 Prominent Short Rate Models 45

    4.4 The Hull-White Model in More Detail 46

    4.5 Trinomial Trees 47

    5 Upwinding Techniques for Short Rate Models 55

    5.1 Derivation of a PDE for Short Rate Models 55

    5.2 Upwind Schemes 56

    5.3 A Puttable Fixed Rate Bond under the Hull-White One Factor Model 63

    6. Boundary, Terminal and Interface Conditions and their Influence 71

    6.1 Terminal Conditions for Equity Options 71

    6.2 Terminal Conditions for Fixed Income Instruments 72

    6.3 Callability and Bermudan Options 74

    6.4 Dividends 74

    6.5 Snowballs and TARNs 75

    6.6 Boundary Conditions 77

    7 Finite Element Methods 81

    7.1 Introduction 81

    7.2 Grid Generation 83

    7.3 Elements 85

    7.4 The Assembling Process 90

    7.5 A Zero Coupon Bond Under the Two Factor Hull-White Model 105

    7.6 Appendix: Higher Order Elements 107

    8 Solving Systems of Linear Equations 117

    8.1 Direct Methods 118

    8.2 Iterative Solvers 122

    9 Monte Carlo Simulation 133

    9.1 The Principles of Monte Carlo Integration 133

    9.2 Pricing Derivatives with Monte Carlo Methods 134

    9.3 An Introduction to the Libor Market Model 139

    9.4 Random Number Generation 146

    10 Advanced Monte Carlo Techniques 161

    10.1 Variance Reduction Techniques 161

    10.2 Quasi Monte Carlo Method 169

    10.3 Brownian Bridge Technique 175

    11 Valuation of Financial Instruments with Embedded American/Bermudan Options within Monte Carlo Frameworks 179

    11.1 Pricing American options using the Longstaff and Schwartz algorithm 179

    11.2 A Modified Least Squares Monte Carlo Algorithm for Bermudan Callable Interest Rate Instruments 181

    11.3 Examples 186

    12 Characteristic Function Methods for Option Pricing 193

    12.1 Equity Models 194

    12.2 Fourier Techniques 201

    13 Numerical Methods for the Solution of PIDEs 209

    13.1 A PIDE for Jump Models 209

    13.2 Numerical Solution of the PIDE 210

    13.3 Appendix: Numerical Integration via Newton-Cotes Formulae 214

    14 Copulas and the Pitfalls of Correlation 217

    14.1 Correlation 218

    14.2 Copulas 221

    15 Parameter Calibration and Inverse Problems 239

    15.1 Implied Black-Scholes Volatilities 239

    15.2 Calibration Problems for Yield Curves 240

    15.3 Reversion Speed and Volatility 245

    15.4 Local Volatility 245

    15.5 Identifying Parameters in Volatility Models 248

    16 Optimization Techniques 253


    16.1 Model Calibration and Optimization 255

    16.2 Heuristically Inspired Algorithms 258

    16.3 A Hybrid Algorithm for Heston Model Calibration 261

    16.4 Portfolio Optimization 265

    17 Risk Management 269

    17.1 Value at Risk and Expected Shortfall 269

    17.2 Principal Component Analysis 276

    17.3 Extreme Value Theory 278

    18 Quantitative Finance on Parallel Architectures 285

    18.1 A Short Introduction to Parallel Computing 285

    18.2 Different Levels of Parallelization 288

    18.3 GPU Programming 288

    18.4 Parallelization of Single Instrument Valuations using (Q)MC 290

    18.5 Parallelization of Hybrid Calibration Algorithms 291

    19 Building Large Software Systems for the Financial Industry 297

    Bibliography 301

    Index 307

  • MICHAEL AICHINGER obtained his Ph.D. in Theoretical Physics from the Johannes Kepler University Linz with a thesis on numerical methods in density functional theory and their application to 2D finite electron systems. A mobility grant led him to the Texas A&M University (2003) and to the Helsinki University of Technology (2004). In 2007 Michael Aichinger joined the Industrial Mathematics Competence Center where he has been working as a senior researcher and consultant in the field of quantitative finance for the last five years. He also works for the Austrian Academy of Sciences at the Radon Institute for Computational and Applied Mathematics where he is involved in several industrial mathematics and computational physics projects. Michael has (co-) authored around 20 journal articles in the fields of computational physics and quantitative finance.

    ANDREAS BINDER obtained his Ph.D. in Industrial Mathematics from the Johannes Kepler University Linz with a thesis on continuous casting of steel. A research grant led him to the Oxford Center for Industrial and Applied Mathematics, UK, in 1991, where he got in touch with mathematical finance for the first time. After some years being an assistant professor at the Industrial Mathematics Institute, in 1996, he left university and became managing director of MathConsult GmbH, where he heads also the Computational Finance Group. Andreas has authored two introductory books on mathematical finance and 25 journal articles in the fields of industrial mathematics and of mathematical finance.

You may also be interested in these books:

Hong Kong Taxation and Tax Planning, 20th Edition
Hong Kong Taxation and Tax Planning, 20th Edition
HKD 370.00
Hong Kong Tax & Accounting Practical Toolkit (Basic Package)
Hong Kong Tax & Accounting Practical Toolkit (Basic Package)
HKD 3,000.00
The Hong Kong Company Secretary's Handbook: Practice and Procedure (11th Edition)
The Hong Kong Company Secretary's Handbook: Practice and Procedure (11th Edition)

List Price: HKD 535.00

HKD 518.95 Save HKD 16.05 (3%)

CPA's Guide to Effective Engagement Letters (14th Edition)
CPA's Guide to Effective Engagement Letters (14th Edition)

List Price: HKD 2,620.00

HKD 2,541.40 Save HKD 78.60 (3%)

Hong Kong Company Law & Compliance Practical Toolkit (Basic Package)
Hong Kong Company Law & Compliance Practical Toolkit (Basic Package)
HKD 4,000.00
PwC Manual of Accounting IFRS 2021 Set
PwC Manual of Accounting IFRS 2021 Set
HKD 2,160.38
China Master Tax Guide 2021 (14th Edition)
China Master Tax Guide 2021 (14th Edition)

List Price: HKD 1,680.00

HKD 1,629.60 Save HKD 50.40 (3%)

Ernst & Young's International GAAP 2021
Ernst & Young's International GAAP 2021

List Price: HKD 2,200.00

HKD 2,134.00 Save HKD 66.00 (3%)

CPA's Guide to Management Letter Comments (2021)
CPA's Guide to Management Letter Comments (2021)

List Price: HKD 4,220.00

HKD 4,093.40 Save HKD 126.60 (3%)

威科先行 • 财税信息库 (双语专业版)
威科先行 • 财税信息库 (双语专业版)
HKD 24,496.00
Accounting Desk Book (2021)
Accounting Desk Book (2021)

List Price: HKD 3,520.00

HKD 3,414.40 Save HKD 105.60 (3%)

Financial Instruments: A Comprehensive Guide to Accounting & Reporting (2021)
Financial Instruments: A Comprehensive Guide to Accounting & Reporting (2021)

List Price: HKD 5,620.00

HKD 5,451.40 Save HKD 168.60 (3%)

China Master GAAP Guide (11th Edition)
China Master GAAP Guide (11th Edition)

List Price: HKD 1,500.00

HKD 1,455.00 Save HKD 45.00 (3%)

Hong Kong Master GAAP Guide, 15th Edition
Hong Kong Master GAAP Guide, 15th Edition

List Price: HKD 1,500.00

HKD 1,455.00 Save HKD 45.00 (3%)

Individual Income Tax Planning for Expatriates in China, 6th Edition
Individual Income Tax Planning for Expatriates in China, 6th Edition

List Price: HKD 1,280.00

HKD 640.00 Save HKD 640.00 (50%)

Hong Kong Company Secretary Checklist
Hong Kong Company Secretary Checklist

List Price: HKD 788.00

HKD 764.36 Save HKD 23.64 (3%)

Concise Guide: Compliance and Company Secretarial Practice of Hong Kong Private Companies (e-Book)
Concise Guide: Compliance and Company Secretarial Practice of Hong Kong Private Companies (e-Book)

List Price: HKD 1,910.00

HKD 1,852.70 Save HKD 57.30 (3%)

Compliance and Company Secretarial Practice of Hong Kong Listed Companies
Compliance and Company Secretarial Practice of Hong Kong Listed Companies

List Price: HKD 1,270.00

HKD 1,231.90 Save HKD 38.10 (3%)