Mamon / Elliott Hidden Markov Models in Finance

Further Developments and Applications, Volume II
1. Auflage 2014
ISBN: 978-1-4899-7442-6
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 209, 261 Seiten

Reihe: International Series in Operations Research & Management Science

Since the groundbreaking research of Harry Markowitz into the application of operations research to the optimization of investment portfolios, finance has been one of the most important areas of application of operations research. The use of hidden Markov models (HMMs) has become one of the hottest areas of research for such applications to finance. This handbook offers systemic applications of different methodologies that have been used for decision making solutions to the financial problems of global markets. As the follow-up to the authors' Hidden Markov Models in Finance (2007), this offers the latest research developments and applications of HMMs to finance and other related fields. Amongst the fields of quantitative finance and actuarial science that will be covered are: interest rate theory, fixed-income instruments, currency market, annuity and insurance policies with option-embedded features, investment strategies, commodity markets, energy, high-frequency trading, credit risk, numerical algorithms, financial econometrics and operational risk.Hidden Markov Models in Finance: Further Developments and Applications, Volume II presents recent applications and case studies in finance and showcases the formulation of emerging potential applications of new research over the book's 11 chapters. This will benefit not only researchers in financial modeling, but also others in fields such as engineering, the physical sciences and social sciences. Ultimately the handbook should prove to be a valuable resource to dynamic researchers interested in taking full advantage of the power and versatility of HMMs in accurately and efficiently capturing many of the processes in the financial market.

Autoren/Hrsg.

Mamon, Rogemar S.

Elliott, Robert J.

Inhaltsverzeichnis

1;Preface;6
2;Contents;10
3;List of Contributors;16
4;Biographical Notes;18
4.1;Editors;18
4.2;Contributors;19
5;1 Robustification of an On-line EM Algorithm for Modelling Asset Prices Within an HMM;24
5.1;1.1 Introduction;24
5.2;1.2 Hidden Markov Model Framework for Asset Returns;26
5.3;1.3 Essential Steps in Elliott's Algorithm;27
5.3.1;1.3.1 Change of Measure;27
5.3.2;1.3.2 Filtering for General Adapted Processes;27
5.3.3;1.3.3 Filter-Based EM Algorithm;30
5.3.4;1.3.4 Summary of Algorithm;31
5.4;1.4 Outliers in Asset Allocation Problem;31
5.4.1;1.4.1 Outliers in General;31
5.4.2;1.4.2 Time-Dependent Context: Exogenous and Endogenous Outliers;32
5.4.3;1.4.3 Evidence for Robustness Issue in Asset Allocation;33
5.5;1.5 Robust Statistics;35
5.5.1;1.5.1 Concepts of Robust Statistics;35
5.5.2;1.5.2 Our Robustification of the HMM: General Strategy;37
5.5.3;1.5.3 Robustification of Step (0);38
5.5.4;1.5.4 Robustification of the E-Step;38
5.5.4.1;1.5.4.1 Crucial Optimality Theorem;39
5.5.4.2;1.5.4.2 Robustification of Steps (RN), (E);39
5.5.5;1.5.5 Robustification of the (M)-Step;41
5.5.5.1;1.5.5.1 Shrinking Neighborhood Approach;41
5.5.5.2;1.5.5.2 Shrinking Neighborhood Approach with Weighted Observations;42
5.5.5.3;1.5.5.3 Robustification of Steps (M1) and (M2);44
5.6;1.6 Implementation and Simulation;46
5.7;1.7 Conclusion;47
5.7.1;1.7.1 Contribution of This Paper;47
5.7.2;1.7.2 Outlook;49
5.8;Appendix;50
5.9;References;52
6;2 Stochastic Volatility or Stochastic Central Tendency: Evidence from a Hidden Markov Model of the Short-Term Interest Rate;55
6.1;2.1 Introduction;55
6.2;2.2 The Model;58
6.3;2.3 Maximum Likelihood Estimation;59
6.4;2.4 The Likelihood Function;59
6.5;2.5 The Interest Rate Model;61
6.6;2.6 Data;62
6.7;2.7 Results;67
6.8;2.8 Conclusion;73
6.9;References;74
7;3 An Econometric Model of the Term Structure of Interest Rates Under Regime-Switching Risk;76
7.1;3.1 Introduction;76
7.2;3.2 The Model;79
7.2.1;3.2.1 A Simple Representation of Markov Regime Shifts;79
7.2.2;3.2.2 Other State Variables;80
7.2.3;3.2.3 The Term Structure of Interest Rates;81
7.2.4;3.2.4 Bond Risk Premiums Under Regime Shifts;82
7.2.5;3.2.5 An Affine Regime-Switching Model;84
7.2.6;3.2.6 The Effects of Regime Shifts on the Yield Curve;87
7.3;3.3 Empirical Results;89
7.3.1;3.3.1 Data and Summary Statistics;89
7.3.2;3.3.2 Estimation Procedure;91
7.3.3;3.3.3 Discussions;95
7.4;3.4 Conclusion;101
7.5;References;101
8;4 The LIBOR Market Model: A Markov-Switching Jump Diffusion Extension;105
8.1;4.1 Introduction;105
8.2;4.2 Mathematical Preliminaries;107
8.3;4.3 The Log-Normal LIBOR Framework;110
8.3.1;4.3.1 An Introduction to the LIBOR Market Model: The Log-Normal Dynamics;111
8.3.2;4.3.2 Pricing of Caps and Floors in the Log-Normal LMM;113
8.4;4.4 The Markov-Switching Jump Diffusion (MSJD) Extension of the LMM;114
8.4.1;4.4.1 Presenting the Extended Framework;115
8.4.2;4.4.2 The Measure Changes and Its Consequences;117
8.4.2.1;4.4.2.1 The Measure Changes, the Wiener Process and the Compensator;117
8.4.2.2;4.4.2.2 The Measure Changes and the Markov Chain;119
8.5;4.5 Pricing in the MSJD Framework;120
8.5.1;4.5.1 Determining the Characteristic Function of YN-1;121
8.5.2;4.5.2 Determining the Characteristic Function of Yj, j=1,…,N-2;125
8.6;4.6 Calibration;125
8.6.1;4.6.1 The Data;126
8.6.2;4.6.2 Discussion of the Results of the Calibration;128
8.6.2.1;4.6.2.1 Most Likely Path and Infinitesimal Generator of the Markov Chain;128
8.6.2.2;4.6.2.2 Parameters Specifying the Compensator Measure with Respect to P;129
8.6.2.3;4.6.2.3 Volatility Parameters in the Model Specification Without Jumps;129
8.6.2.4;4.6.2.4 Final Estimates for Volatility and Jump Parameters;131
8.7;4.7 Conclusion;132
8.8;References;134
9;5 Exchange Rates and Net Portfolio Flows: A Markov-Switching Approach;137
9.1;5.1 Introduction;137
9.2;5.2 The Model;139
9.3;5.3 Data;140
9.4;5.4 Empirical Results;142
9.5;5.5 Conclusions;149
9.6;References;150
10;6 Hedging Costs for Variable Annuities Under Regime-Switching;153
10.1;6.1 Introduction;154
10.2;6.2 Hedging Costs;156
10.2.1;6.2.1 Derivation of the Pricing Equation;157
10.2.2;6.2.2 Events;159
10.2.2.1;6.2.2.1 Event Times;159
10.2.2.2;6.2.2.2 Withdrawal Strategy;159
10.2.2.3;6.2.2.3 Bonus;160
10.2.2.4;6.2.2.4 Withdrawal Not Exceeding the Contract Rate;160
10.2.2.5;6.2.2.5 Partial or Full Surrender;160
10.2.2.6;6.2.2.6 Ratchets;161
10.2.2.7;6.2.2.7 Simultaneous Events;161
10.2.3;6.2.3 Loss-Maximizing Strategies;161
10.2.4;6.2.4 Regime-Switching;162
10.3;6.3 Optimal Consumption;163
10.3.1;6.3.1 Utility PDE;164
10.3.2;6.3.2 Events;164
10.3.3;6.3.3 Consumption-Optimal Withdrawal;165
10.3.4;6.3.4 Regime-Switching;166
10.3.5;6.3.5 Hyperbolic Absolute Risk-Aversion;167
10.4;6.4 Numerical Method;167
10.4.1;6.4.1 Homogeneity;167
10.4.2;6.4.2 Localized Problem and Boundary Conditions;170
10.4.3;6.4.3 Determining the Hedging Cost Fee;171
10.5;6.5 Results;171
10.5.1;6.5.1 Loss-Maximizing and Contract Rate Withdrawal;171
10.5.1.1;6.5.1.1 Withdrawal Analysis;172
10.5.1.2;6.5.1.2 Management Rate;174
10.5.1.3;6.5.1.3 Alternate Fee Structure;174
10.5.2;6.5.2 Consumption-Optimal Withdrawal;174
10.5.2.1;6.5.2.1 Risk-Aversion;175
10.5.2.2;6.5.2.2 Taxation;177
10.6;6.6 Conclusion;179
10.7;Appendix;180
10.8;References;185
11;7 A Stochastic Approximation Approach for Trend-FollowingTrading;187
11.1;7.1 Introduction;187
11.2;7.2 Problem Formulation;188
11.3;7.3 Asymptotic Properties;191
11.4;7.4 Numerical Examples;196
11.5;References;203
12;8 A Hidden Markov-Modulated Jump Diffusion Model for EuropeanOption Pricing;205
12.1;8.1 Introduction;205
12.2;8.2 Hidden Regime-Switching Jump-Diffusion Market;208
12.3;8.3 Filtering Theory and Filtered Market;212
12.3.1;8.3.1 The Separation Principle;212
12.3.2;8.3.2 Filtering Equations;214
12.4;8.4 Generalized Esscher Transform in the Filtered Market;218
12.5;8.5 European-Style Option;223
12.6;8.6 Conclusion;227
12.7;References;227
13;9 An Exact Formula for Pricing American Exchange Options with Regime Switching;230
13.1;9.1 Introduction;230
13.2;9.2 Asset Price Dynamics;232
13.3;9.3 Problem Formulation;234
13.4;9.4 A Closed-Form Formula;238
13.5;9.5 Conclusion;243
13.6;References;243
14;10 Parameter Estimation in a Weak Hidden Markov Modelwith Independent Drift and Volatility;246
14.1;10.1 Introduction;246
14.2;10.2 Modelling Background;249
14.3;10.3 Filters and Parameter Estimation;250
14.4;10.4 Numerical Implementation;254
14.5;10.5 Conclusion;258
14.6;References;258
15;11 Parameter Estimation in a Regime-Switching Modelwith Non-normal Noise;260
15.1;11.1 Introduction;260
15.2;11.2 Model Set Up;261
15.3;11.3 Reference Probability Measure;262
15.4;11.4 Recursive Estimation;263
15.5;11.5 Parameter Estimation;265
15.5.1;11.5.1 EM Algorithm and the Estimation of Transition Probabilities;266
15.5.2;11.5.2 Student's t-Distributed Noise Term;267
15.6;11.6 Numerical Application of the Filters;271
15.6.1;11.6.1 Filtering Using Simulated Data;271
15.6.2;11.6.2 Application of the Filters to Observed Market Data;277
15.7;11.7 Conclusions;279
15.8;References;280