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Risk Management and Value
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Risk Management
and Value
Valuation and Asset Pricing
World Scientific Studies in International Economics
(ISSN: 1793-3641)
Series Editor Robert M. Stern, University of Michigan, USA
Editorial Board Vinod K. Aggarwal, University of California-Berkeley, USA
Alan Deardorff, University of Michigan, USA
Paul DeGrauwe, Katholieke Universiteit Leuven, Belgium
Barry Eichengreen, University of California-Berkeley, USA
Mitsuhiro Fukao, Keio University, Tokyo, Japan
Robert L. Howse, University of Michigan, USA
Keith E. Maskus, University of Colorado, USA
Arvind Panagariya, Columbia University, USA
Published
Vol. 1 Cross-Border Banking: Regulatory Challenges
edited by Gerard Caprio, Jr (Williams College, USA),
Douglas D. Evanoff (Federal Reserve Bank of Chicago, USA) &
George G. Kaufman (Loyola University Chicago, USA)
Vol. 2 International Financial Instability: Global Banking and National Regulation
edited by Douglas E. Evanoff (Federal Reserve Bank of Chicago, USA),
George G. Kaufman (Loyola University Chicago, USA) &
John Raymond LaBrosse (Int’l Assoc. of Deposit Insurers, Switzerland)
Vol. 3 Risk Management and Value: Valuation and Asset Pricing
edited by Mondher Bellalah, Jean Luc Prigent, Annie Delienne
(Université de Cergy-Pontoise, France),
Georges Pariente (Institut Supérieur de Commerce, ISC Paris, France),
Olivier Levyne, Michel Azria (ISC Paris, France) &
Jean Michel Sahut (ESC Amiens, France)
Forthcoming
Globalization and International Trade Policies
by Robert M. Stern (University of Michigan, USA)
Emerging Markets
by Ralph D. Christy (Cornell University, USA)
Institutions and Gender Empowerment in the Global Economy: An Overview
of Issues (Part I & Part II)
by Kartik C. Roy (University of Queensland, Australia)
Cal Clark (Auburn University, USA) &
Hans C. Blomqvist (Swedish School of Economics and Business
Adminstration, Finland)
The Rules of Globalization (Casebook)
by Rawi Abdelal (Harvard Business School, USA)
YiShen - Risk Management & value.pmd 2 5/20/2008, 6:26 PM
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
World Scientific
World Scientific
Studies in
International 3 Economics
Risk Management
and Value
Valuation and Asset Pricing
Editors
Mondher Bellalah
Université de Cergy-Pontoise, France
Jean-Luc Prigent
Université de Cergy-Pontoise, France
Jean-Michel Sahut
ESC Amiens, France
Associate Editors
Georges Pariente
Institut Supérieur de Commerce Paris, France
Olivier Levyne
Institut Supérieur de Commerce Paris, France
Michel Azaria
Institut Supérieur de Commerce Paris, France
Annie Delienne
Université de Cergy-Pontoise, France
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
For photocopying of material in this volume, please pay a copying fee through the Copyright
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to
photocopy is not required from the publisher.
ISBN-13 978-981-277-073-8
ISBN-10 981-277-073-9
Typeset by Stallion Press
Email: [email protected]
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
Copyright © 2008 by World Scientific Publishing Co. Pte. Ltd.
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
Printed in Singapore.
World Scientific Studies in International Economics — Vol. 3
RISK MANAGEMENT AND VALUE
Valuation and Asset Pricing
YiShen - Risk Management & value.pmd 1 5/20/2008, 6:26 PM
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CONTENTS
Introduction ix
Chapter 1. Managing Derivatives in the Presence of a
Smile Effect and Incomplete Information
1
Mondher Bellalah
Chapter 2. A Value-at-Risk Approach to Assess Exchange
Risk Associated to a Public Debt Portfolio:
The Case of a Small Developing Economy
11
Wissem Ajili
Chapter 3. A Method to Find Historical VaR for Portfolio
that Follows S&P CNX Nifty Index by
Estimating the Index Value
61
K. V. N. M. Ramesh
Chapter 4. Some Considerations on the Relationship
between Corruption and Economic Growth
71
Victor Dragota, Laura Obreja Bra¸ ˇ soveanu and
Andreea Semenescu
Chapter 5. Financial Risk Management by Derivatives
Caused from Weather Conditions: Its
Applicability for Türk˙iye
97
Turgut Özkan
v
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vi CONTENTS
Chapter 6. The Basel II Framework Implementation and
Securitization
117
Marie-Florence Lamy
Chapter 7. Stochastic Time Change, Volatility, and
Normality of Returns: A High-Frequency Data
Analysis with a Sample of LSE Stocks
129
Olfa Borsali and Amel Zenaidi
Chapter 8. The Behavior of the Implied Volatility Surface:
Evidence from Crude Oil Futures Options
151
Amine Bouden
Chapter 9. Procyclical Behavior of Loan Loss Provisions
and Banking Strategies: An Application to the
European Banks
177
Didelle Dilou Dinamona
Chapter 10. Market Power and Banking Competition on
the Credit Market
205
Ion Lapteacru
Chapter 11. Early Warning Detection of Banking
Distress — Is Failure Possible for European
Banks?
231
Anissa Naouar
Chapter 12. Portfolio Diversification and Market Share
Analysis for Romanian Insurance Companies
277
Mihaela Dragota, Cosmin Iuliu S ˘ . erbanescu and ˘
Daniel Traian Pele
Chapter 13. On the Closed-End Funds Discounts/
Premiums in the Context of the Investor
Sentiment Theory
299
Ana Paula Carvalho do Monte and
Manuel José da Rocha Armada
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CONTENTS vii
Chapter 14. Why has Idiosyncratic Volatility Increased in
Europe?
337
Jean-Etienne Palard
Chapter 15. Debt Valuation, Enterprise Assessment and
Applications
379
Didier Vanoverberghe
Chapter 16. Does The Tunisian Stock Market Overreact? 437
Fatma Hammami and Ezzeddine Abaoub
Chapter 17. Investor–Venture Capitalist Relationship:
Asymmetric Information, Uncertainty, and
Monitoring
463
Mondher Cherif and Skander Sraieb
Chapter 18. Threshold Mean Reversion in Stock Prices 477
Fredj Jawadi
Chapter 19. Households’ Expectations of Unemployment:
New Evidence from French Microdata
495
Salah Ghabri
Chapter 20. Corporate Governance and Managerial Risk
Taking: Empirical Study in the Tunisian
Context
511
Amel Belanes Aroui and Fatma Wyème Ben Mrad
Douagi
Chapter 21. Nonlinearity and Genetic Algorithms in the
Decision-Making Process
541
Nizar Hachicha and Abdelfettah Bouri
Chapter 22. ICT and Performance of the Companies: The
Case of the Tunisian Companies
563
Jameleddine Ziadi
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viii CONTENTS
Chapter 23. Option Market Microstructure 581
Jean-Michel Sahut
Chapter 24. Does the Standardization of Business Processes
Improve Management? The Case of Enterprise
Resource Planning Systems
601
Tawhid Chtioui
Chapter 25. Does Macroeconomic Transparency Help
Governments be Solvent? Evidence from
Recent Data
615
Ramzi Mallat and Duc Khuong Nguyen
Index 633
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INTRODUCTION
This book is devoted to selected papers from the International Finance Conference, IFC4, held during 15–17 March 2007, in Hammamet, Tunisia
under the authority of the Ministry of Higher Education, Technology and
Scientific Research and in cooperation with the Association Française de
Finance (AFFI), Association Méditerranéenne de Finance, Assurance et Management, AMFAM, http://amfam.France-paris.org, the Network “Réseau
Euro-Méditérranéen”, http://remereg.France-paris.org.
The Organizing Committee from University of Cergy and ISC Paris,
in collaboration with local organizers, FSEG Tunis, University of Tunis
7 November, and Universities of Sfax and Sousse and UMLT Nabeul
(www.umlt.ens.tn) have done an excellent job in managing the different aspects
of the conference.
We would like to thank our members of the committee and in particular our keynote speakers, Nobel Laureates James Heckman (USA) and Harry
Markowitz (USA), and the main speakers such as George Constantinides (University of Chicago, USA), Dilip Ghosh (USA), Ephraim Clark (Middlesex
University, UK), Gérard Hirigoyen (University of Bordeaux 4, France), and
many others.
The conference attracted nearly 1,200 participants. Due to space constraints, the committee is obliged to select only some of the papers presented
in the conference. In collaboration with the members of the scientific committee, the papers come from different fields covering value, volatility, and
risk management in a range of areas.
We would like to thank finally the Minister of Higher Education, Technology and Scientific Research, Professor Lazhar Bououny; the Minister,
Governor of the Central Bank, Toufik Baccar; the Secretary of State for
ix
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x INTRODUCTION
Scientific Research, Ridha Mesbah; the Tunisian Government and in particular the President Zine El Abidine Ben Ali, for his role in the success of the
Fourth International Finance Conference (IFC4).
Mondher Bellalah
Conference President, President AMFAM, President of the Network
REMEREG THEMA, and ISC Group, Paris.
“This conference brought together leading scholars of Economics and Finance
from around the world. It provided an opportunity to exchange ideas across
diverse fields. The discussions were at a high level and the setting was very
beautiful. The organizers are to be praised for convening such an excellent
conference.”
James Heckman
Professor in Economics and the College, University of Chicago. Awarded
Nobel Prize in Economic Sciences in 2000.
“I spoke to the Conference briefly via satellite. I used the fact that I was in San
Diego and the Conference in Tunis to illustrate Adam Smith’s observations
concerning the importance of large markets. You can hardly imagine a larger
market than the one which ties San Diego directly to Tunis and anywhere else
in the world. You do not need video conferencing equipment to participate
in this market. Frequently a cell phone will do. At first information flows, but
then often goods follow. I tied this to the theme of the conference. I wish to
thank the sponsors and organizers of the Conference, those who assisted me
in speaking to it from San Diego, and those who asked great questions at the
end of my talk.”
Harry Markowitz
Professor of Finance, Rady School of Management, University of California,
San Diego. Awarded Nobel Prize in Economic Sciences in 1990.
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CHAPTER 1
MANAGING DERIVATIVES IN THE
PRESENCE OF A SMILE EFFECT AND
INCOMPLETE INFORMATION
Mondher Bellalah∗
This chapter develops a simple option pricing model when markets can make
sudden jumps in the presence of incomplete information. Incomplete information can be defined in the context of Merton’s (1987) model of capital market
equilibrium with incomplete information. In this context, analytic formulas
can be derived for options using the Black–Scholes (1973) approach as in
Bellalah (1999). The option value depends upon the probability and magnitude of jumps and a continuous volatility. The model is useful in explaining
the smile effect and in extracting information costs. The model can be applied
to hedging strategies for different strike prices and can be used for the valuation of different types of options.a It can also be used in the identification of
mispriced options. Some simulations are run with and without shadow costs
of incomplete information. We run some simulations to extract information
costs using market data. Our model can be used to estimate information costs
in different markets.
1 Introduction
This chapter develops a simple option pricing model when markets can make
sudden jumps in the presence of incomplete information. We build on Derman
et al. (1991) modeling of jumps on the underlying asset and combine it with
the Bellalah (1999) approach to include information costs.
∗THEMA, University of Cergy and ISC Paris.
aMany thanks to Riva F, for his help in running simulations.
1
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2 M. BELLALAH
These costs are defined with respect to Merton’s (1987) simple model of
capital market equilibrium with incomplete information: investors spend time
and money to gather information about the financial instruments and financial
markets.
The structure of the chapter is as follows. Section 2 explains the role of
information costs in asset pricing and option pricing with respect to Merton’s
model of capital market equilibrium with incomplete information. In Sec. 3,
we present the model we use for the valuation of option prices on the S&P
500 index when prices can jump and information costs are taken into account.
The results of our simulations are presented in Sec. 4. Section 5 summarizes
and concludes the chapter.
2 Option Pricing in the Presence of Information Costs
Differences in information can explain some puzzling phenomena in finance
such as the “home equity bias” or the “weekend effect.” Information costs
can also offer an explanation for limited participation in financial markets. In
general, a fixed cost to participate in the stock market is viewed as summarizing
both transaction (as brokerage fees) and information costs (such as the cost of
understanding financial institutions, the cost of gathering information about
assets, etc.).
Merton (1987) adopts most of the assumptions of the original Capital Asset
Pricing Model (CAPM) and relaxes the assumption of equal information across
investors. Besides, he assumes that investors hold only securities of which they
are aware. This assumption is motivated by the observation that portfolios held
by actual investors include only a small fraction of all available traded securities.
The story of information costs applies in varying degrees to the adoption
in practice of new structural models of evaluation, i.e. option pricing models.
It applies also to the diffusion of innovations for several products and technologies. The recognition of the different speeds of information diffusion is
particularly important in explaining the behavior of different firms.
In Merton’s model, the expected returns increase with systematic risk,
firm-specific risk, and relative market value. The expected returns decrease
with relative size of the firm’s investor base, referred to in Merton’s model as
the “degree of investor recognition”.
The analysis of investment opportunities can be done in a standard option
framework “à la Black–Scholes” (1973). These authors derive their model
under the assumption that investors create riskless hedges between options
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MANAGING DERIVATIVES IN THE PRESENCE OF A SMILE EFFECT 3
and their underlying securities. Besides, their formula relies implicitly on the
CAPM.
Merton’s model may be stated as follows:
RS − r = βS [Rm − r] + λS − βSλm,
where
RS : the equilibrium expected return on an asset S;
Rm: the equilibrium expected return on the market portfolio;
r: the riskless rate of interest;
RS : cov(RS /Rm)/var(Rm);
λS : the equilibrium aggregate “shadow cost” for the asset S, which is of the
same dimension as the expected rate of return on the asset S; and
λm: the weighted average shadow cost of incomplete information over all
assets.
Bellalah and Jacquillat (1995) and Bellalah (1999) provide a valuation
formula for commodity options in the context of incomplete information.
Their analysis is based on Merton’s (1987) model and can be used to extend
the analysis by Derman et al. (1991). This is the goal of the following section.
3 Valuing Options When Markets Can Jump in the Presence of
Shadow Costs of Incomplete Information
We first briefly present how to integrate market jumps in a simple way and
then extend the analysis to take into account information costs.
3.1 Valuing Options When Market Can Jump
Consider the following simple model proposed by Derman et al. (1991). The
underlying asset price at time 0 today is S. In the next instant, the underlying
asset price can jump up by u% to Su with probability w or down by d% to
Sd with probability (1 − w).
The probability w is expected to be close to 0 or 1. This means that either
a jump up or a jump down predominates. After the first jump, the underlying
asset will diffuse with constant volatility σ as in the Black–Scholes (1973)
model. No other jumps will occur.
The value of any security in this model can be computed as the average of
its payoffs over the scenarios where the underlying asset jumps up or down.
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4 M. BELLALAH
Hence, the option value is given by
Option = wBS(Su, K , σ,r, δ, T ) + (1 − w)BS(Sd , K , σ,r, δ, T ), (1)
where BS(S, K , σ,r, δ, T ) is the formula by Black–Scholes (1973) and δ refers
to the continuous dividend yield. This is the formula that appears in the work
by Derman et al. (1991).
The values used for the underlying asset are:
Su = S(1 + u); Sd = S(1 − d ).
The current value of the underlying asset corresponds also to an average value
after a jump up and a jump down. Hence, the jump up and the jump down
are related by
d (1 − w) = wu.
3.2 Extension with Information Costs
The extension of the jump model in the presence of shadow costs can be easily
done. The value of any security in this model can be computed as the average of its payoffs over the scenarios where the underlying asset jumps up or
down. This process corresponds to a continuous diffusion which is accompanied occasionally by a jump. The use of the Black–Scholes (1973) model
assumes that all future variation in the underlying asset value is attributed to
the continuous diffusion and none to the discontinuous jump.
The jump-diffusion process is defined by a diffusion volatility and a probability and magnitude for the discontinuous jump. The diffusion volatility
characterizes the continuous diffusion. A small probability of a jump of the
underlying asset price in the direction of the strike price can affect the value of
an out-of-the-money option. In the presence of such a process, two options at
least are necessary to extract information about the implied volatility and the
implied jump. The model parameters are such that the model error, i.e. the
sum of the squared difference between the model prices and the market prices
for the two options are as close as possible to zero.
The same approach can be extended to allow the estimation of implied
information costs from market data.
In our analysis, the option value is given by
option = wBS(Su, K , σ,r, δ, λs, λc, T )
+ (1 − w)BS(Sd , K , σ,r, δ, λs, λc, T ), (2)
where BS(Su, K , σ,r, δ, λs, λc, T ) is the formula given by Bellalah (1999).