Capital Account Liberation: Methods and Applications

432 Pages·2015·5.301 MB·English

by  Ying Yirong, Jeffrey Yi-Lin Forrest

Business Management / Economics FY
o Systems Evaluation, Prediction, and Decision-Making Series
i
rr
ro
Along with the development of economic globalization, many countries have en
begun to relax their controls on their capital accounts. However, the recent financial sg CAPITAL ACCOUNT
t
crises in Latin American countries as well as the exchange rate crises in Southeast
Asian countries have shown that there is major risk associated with capital account
liberalization. LIBERATION
C
This book details the benefits and risks of capital account liberalization and A
explains how to take an open-door policy at the appropriate time in order to reduce
P Methods and Applications
the risk to the lowest possible level. Supplying a complete mathematical analysis
I
framework for the study of the problem of capital account liberalization, it presents
T
a few important models that have been developed for the study of capital account
A
liberalization.
L

Next, the book examines the influence of capital account liberalization on the
A
stability of financial markets by greatly expanding the scope of ordinary differential
C
equation theory to the analysis of local stabilities. It conveys cutting-edge results
while providing a general yet simple analysis framework, enriched with practical C
experiences from developing countries.
O
This book applies the theory of limit cycles to the study of problems related to U
capital account liberalization and discusses the contagion of financial crises among
N
different countries. Many problems related to capital account liberalization are
formulated as optimization models, showing the fact that much broader economic T
issues can be solved by employing optimization methods.
L
I
The book concludes by comparing the contagion effect of financial markets
B
between nations with a relatively high degree of openness with those characterized
E
by a moderate degree of openness. Explaining how to determine optimal capital
inflows and outflows, this book provides you with the understanding required to R
accurately determine the characteristics, backgrounds, causes, and roles of capital
A
account liberalization and relevant capital flows.
T
I
O
N
K25108
6000 Broken Sound Parkway, NW Ying Yirong • Jeffrey Yi-Lin Forrest
Suite 300, Boca Raton, FL 33487 ISBN: 978-1-4987-1226-2
711 Third Avenue 90000
New York, NY 10017
an informa business
2 Park Square, Milton Park
www.crcpress.com Abingdon, Oxon OX14 4RN, UK
9 781498 712262
w w w. c r c p r e s s . c o m
K25108 cvr mech.indd 1 4/9/15 11:03 AM

Capital Account
Liberation
Methods and Applications
Systems Evaluation, Prediction, and Decision-Making Series
Series Editor
Yi Lin, PhD
Professor of Systems Science and Economics
School of Economics and Management
Nanjing University of Aeronautics and Astronautics

Capital Account Liberation: Methods and Applications
Ying Yirong and Jeffrey Yi-Lin Forrest
ISBN 978-1-4987-1226-2
Grey Game Theory and Its Applications in Economic Decision-Making
Zhigeng Fang, Sifeng Liu, Hongxing Shi, and Yi Lin
ISBN 978-1-4200-8739-0
Hybrid Rough Sets and Applications in Uncertain Decision-Making
Lirong Jian, Sifeng Liu, and Yi Lin
ISBN 978-1-4200-8748-2
Introduction to Theory of Control in Organizations
Vladimir N. Burkov, Mikhail Goubko, Nikolay Korgin, and Dmitry Novikov
ISBN 978-1-4987-1423-5
Investment and Employment Opportunities in China
Yi Lin and Tao Lixin
ISBN 978-1-4822-5207-1
Irregularities and Prediction of Major Disasters
Yi Lin
ISBN: 978-1-4200-8745-1
Measurement Data Modeling and Parameter Estimation
Zhengming Wang, Dongyun Yi, Xiaojun Duan, Jing Yao, and Defeng Gu
ISBN 978-1-4398-5378-8
Optimization of Regional Industrial Structures and Applications
Yaoguo Dang, Sifeng Liu, and Yuhong Wang
ISBN 978-1-4200-8747-5
Systems Evaluation: Methods, Models, and Applications
Sifeng Liu, Naiming Xie, Chaoqing Yuan, and Zhigeng Fang
ISBN 978-1-4200-8846-5
Systemic Yoyos: Some Impacts of the Second Dimension
Yi Lin
ISBN 978-1-4200-8820-5
Theory and Approaches of Unascertained Group Decision-Making
Jianjun Zhu
ISBN 978-1-4200-8750-5
Theory of Science and Technology Transfer and Applications
Sifeng Liu, Zhigeng Fang, Hongxing Shi, and Benhai Guo
ISBN 978-1-4200-8741-3
Capital Account
Liberation
Methods and Applications
Ying Yirong • Jeffrey Yi-Lin Forrest
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does
not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MAT-
LAB® software or related products does not constitute endorsement or sponsorship by The MathWorks
of a particular pedagogical approach or particular use of the MATLAB® software.
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2015 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20150409
International Standard Book Number-13: 978-1-4987-1227-9 (eBook - PDF)
This book contains information obtained from authentic and highly regarded sources. Reasonable
efforts have been made to publish reliable data and information, but the author and publisher cannot
assume responsibility for the validity of all materials or the consequences of their use. The authors and
publishers have attempted to trace the copyright holders of all material reproduced in this publication
and apologize to copyright holders if permission to publish in this form has not been obtained. If any
copyright material has not been acknowledged please write and let us know so we may rectify in any
future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced,
transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or
hereafter invented, including photocopying, microfilming, and recording, or in any information stor-
age or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copy-
right.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222
Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that pro-
vides licenses and registration for a variety of users. For organizations that have been granted a photo-
copy license by the CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are
used only for identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Contents
Preface .........................................................................................................xiii
Acknowledgments ........................................................................................xix
Authors .........................................................................................................xxi
1 From Theory to Visualization: General Analysis
Framework in Finance ............................................................................1
1.1 Mathematical Applications in Finance ..............................................1
1.1.1 Synergetic Approach .............................................................4
1.2 Mathematical Models in Finance ....................................................11
1.3 Mathematical Principles in Finance .................................................17
1.3.1 Financial Balances Equation ...............................................17
1.3.2 A Model in Canonical Form ...............................................18
1.3.3 Rationality of Behavior .......................................................20
1.3.4 Rational Expectations Principle ..........................................21
1.3.5 Model of the Russian Economy in the Crisis Period ...........24
1.3.6 Model of the Japanese Economy in the Crisis Period ..........27
1.4 Mathematical Estimations in Finance .............................................29
1.4.1 Introduction .......................................................................29
1.4.2 Estimation ..........................................................................31
1.4.3 Conclusions ........................................................................33
1.5 Mathematical Approximations in Finance ......................................34
1.5.1 Introduction .......................................................................35
1.5.2 Main Results ......................................................................36
1.5.3 Conclusions .......................................................................40
1.6 Game Theory in Finance ................................................................40
1.6.1 Model Assumptions ............................................................41
1.6.2 Evolutionary Game Model ................................................42
1.6.3 Stability Analysis ...............................................................44
1.6.4 Model Summary .................................................................50
1.7 Visualization Technology in Finance ...............................................51
1.7.1 Introduction .......................................................................51
v
vi ◾ Contents
1.7.2 Self-Organizing Maps .........................................................52
1.7.3 Clustering of the SOM .......................................................54
1.7.4 Identifying Systemic Financial Crises .................................55
2 From Micheal to Heckscher–Ohlin: ODE for Capital
Account Liberation ...............................................................................57
2.1 General Theory of Ordinary Differential Equations ........................57
2.1.1 Basic Concepts of Ordinary Differential Equations ............57
2.1.1.1 Equation with Separated Variables: y′ = f(x)g(y) ......59
2.1.1.2 Homogeneous Differential Equation: y′ = f(y/x) .....60
2.1.1.3 Fractional Homogeneous Differential
⎛ ax+by+c ⎞
Equation: yʹ= f ⎜ ⎟ ..........................60
⎝αx+βy+γ⎠
2.1.1.4 The Logistic Equation .........................................61
2.1.1.5 Homogeneous Equation: Ly := y′ + g(x)y = 0 .........62
2.1.1.6 Nonhomogeneous Equation: Ly = h(x) .................63
2.1.1.7 Bernoulli’s Equation: y′ + g(x)y + h(x)yα = 0, α ≠ 1 .....64
2.1.1.8 Riccati’s Equation: y′ + g(x)y + h(x)y2 = k(x) ..........64
2.1.2 Systems with Constant Coefficients ....................................65
2.1.2.1 Real Normal Forms ............................................67
2.1.2.2 Stability ..............................................................69
2.2 Dynamic Path of Nonperforming Loans: First-Order ODE ............70
2.2.1 Introduction .......................................................................70
2.2.2 Hypothesis ..........................................................................71
2.2.3 The Model ..........................................................................73
2.2.4 Analysis ..............................................................................74
2.2.5 Conclusions ........................................................................75
2.3 Stock Market’s Liquidity Risk: Second-Order ODE .......................77
2.3.1 Introduction ......................................................................77
2.3.2 The Model ..........................................................................78
2.3.3 Exogenous Shocks ..............................................................80
2.3.4 Numerical Example ............................................................82
2.4 Stability of Michael Model under Capital Control:
Two-Dimensional Systems (I) ..........................................................85
2.4.1 Introduction .......................................................................85
2.4.2 The Model ..........................................................................87
2.4.3 Stability Analysis ................................................................89
2.4.4 Conclusions ........................................................................96
2.5 Exchange Rate Fluctuations under Capital Control:
Two-Dimensional Systems (II) ........................................................96
2.5.1 Introduction .......................................................................96
2.5.2 Stability Analysis ................................................................97
2.5.3 Conclusions ......................................................................101
Contents ◾ vii
2.6 Dynamic Optimization of Competitive Agents:
Three-Dimensional Systems ...........................................................102
2.6.1 Introduction .....................................................................102
2.6.2 The Model ........................................................................103
2.6.3 Analysis ............................................................................105
2.6.4 Conclusions ......................................................................108
2.7 Dynamic Heckscher–Ohlin Model: Four-Dimensional Systems ......108
2.7.1 Introduction .....................................................................108
2.7.2 The Model ........................................................................109
2.7.3 Local Stability Analysis ....................................................111
2.7.4 Conclusions ......................................................................112
2.8 Instability: Risk of Capital Flow ....................................................113
2.8.1 Introduction .....................................................................113
2.8.2 Instability σ ......................................................................114
2.8.2.1 σ−g Relations ....................................................114
2.8.2.2 Trade-Off Optimization ...................................116
2.8.2.3 b-Effect and c-Effect .........................................119
2.8.3 Empirical Examples ..........................................................120
2.8.4 Conclusion .......................................................................122
3 From European to Asian Option: PDE
for Capital Account Liberation ..........................................................123
3.1 General Method of Parabolic Partial Differential Equations of
Second Order ................................................................................123
3.2 Pricing of Carbon Emission Cost: Linear Parabolic PDEs (I) ........126
3.2.1 Introduction .....................................................................127
3.2.2 The Model ........................................................................129
3.2.3 The Calculation ................................................................131
3.2.4 Conclusions ......................................................................137
3.3 Pricing of Foreign Currency Option: Linear Parabolic PDEs (II) ......137
3.3.1 Introduction .....................................................................137
3.3.2 The Model ........................................................................138
3.3.3 The Solution .....................................................................139
3.4 Pricing of Credit Default Swaps: Linear Parabolic PDEs (III) .......142
3.4.1 Introduction .....................................................................142
3.4.2 The Model ........................................................................144
3.4.3 The Solution .....................................................................147
3.5 Pricing of Forward Exchange Rate: Linear Parabolic PDEs (IV) .......150
3.6 Pricing of Arithmetic Average Asian Option: Nonlinear
Parabolic PDEs(I) ..........................................................................155
3.6.1 Introduction .....................................................................155
3.6.2 The Lemma ......................................................................156
viii ◾ Contents
3.6.3 Decomposition of the Solution .........................................158
3.6.4 Estimation for Error .........................................................161
3.6.5 Estimation of the Error Term ...........................................162
3.6.6 Conclusions ......................................................................169
3.7 Pricing of European Exchange Options: Nonlinear
Parabolic PDEs (II) .......................................................................170
3.7.1 Introduction .....................................................................170
3.7.2 Foreign Exchange Option with Fractional
Brownian Motion .............................................................172
3.7.3 Conclusions ......................................................................175
4 From Financial Crises to Currency Substitution: Limit Cycle
Theory for Capital Account Liberation ..............................................177
4.1 General Theory of Limit Cycles .....................................................177
4.2 Poincaré Problem: Quadratic Polynomial Differential
Systems (I) ..................................................................................180
4.2.1 Introduction .....................................................................180
4.3 Foreign Assets and Foreign Liabilities: Quadratic
Polynomial Differential Systems (II) ..............................................183
4.3.1 Introduction .....................................................................183
4.3.2 Macroeconomic Model .....................................................183
4.3.3 Dynamics Analysis ...........................................................185
4.3.4 Conclusion .......................................................................187
4.4 Dynamics of Employment: Cubic Polynomial
Differential Systems (I) ..................................................................188
4.4.1 Introduction .....................................................................188
4.4.2 Model ...............................................................................189
4.4.3 Calculation .......................................................................190
4.4.4 Conclusions ......................................................................193
4.5 Contagion of Financial Crisis: Cubic Polynomial
Differential Systems (II) ................................................................194
4.5.1 Introduction .....................................................................194
4.5.2 Model ...............................................................................195
4.5.3 Analysis ............................................................................197
4.5.4 Conclusions ......................................................................201
4.6 Contagion of Currency Crises: Fractional Differential
Systems (I)..................................................................................202
4.6.1 Introduction .....................................................................202
4.6.2 Model and Analysis .........................................................206
4.6.3 Conclusions ......................................................................209
4.7 Contagion of Currency Crises with Extra-Absorption:
Fractional Differential Systems (II) ................................................210