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prices might have already grown in anticipation of this event. Then

investors may start immediate profit taking, which leads to falling prices.

2. In the case with g < 0, the system has an energy source and the trajectory

is an unbounded outward spiral.

CHAPTER 8

1. See, for example, [1] and references therein. Note that the GARCH

models generally assume that the unconditional innovations are

normal.

2. While several important findings have been reported after publishing

[2], I think this conclusion still holds. On a philosophical note, statistical

data analysis in general is hardly capable of attaining perfection of

mathematical proof. Therefore, scholars with the â€˜â€˜hard-scienceâ€™â€™

147

Comments

background may often be dissatisfied with rigorousness of empirical

research.

3. There has been some interesting research on the distribution of the

company sizes [3, 4].

4. The foreign exchange data available to academic research are overwhelm-

ingly bank quotes (indicative rates) rather than the real inter-bank trans-

action rates (so-called firm rates) [5].

CHAPTER 9

1. In financial literature, derivatives are also called contingent claims.

2. The names of the American and European options refer to the exercising

rule and are not related to geography. Several other types of options with

complicated payoff rules (so-called exotic options) have been introduced

in recent years [1Ã€3].

3. The U.S. Treasury bills are often used as a benchmark for the risk-free

asset.

4. Here and further, the transaction fees are neglected.

Ã€1

@F

5. We might choose also one share and Ã€ options.

@S

CHAPTER 10

1. See Chapter 11.

2. Qualitative graphical presentation of the efficient frontier and the capital

market line is similar to the trade-off curve and the trade-off straight line,

respectively, depicted in Figure 10.1.

3. Usually, Standard and Poorâ€™s 500 Index is used as proxy for the U.S.

market portfolio.

4. ROE Â¼ E/B where E is earnings; B is the book value that in a nutshell

equals the companyâ€™s assets minus its debt.

CHAPTER 11

1. In risk management, the self-explanatory notion of P/L is used rather

than return.

2. In the current literature, the following synonyms of ETL are sometimes

used: expected shortfall and conditional VaR [2].

3. EWMA or GARCH are usually used for the historical volatility forecasts

(see Section 4.3).

148 Comments

CHAPTER 12

1. Lots of useful information on agent-based computational economics are

present on L. Tesfatsionâ€™s website: http://www.econ.iastate.edu/tesfatsi/

ace.htm. Recent developments in this field can also be found in the

materials of the regularly held Workshops on Economics and Heteroge-

neous Interacting Agents (WEHIA), see, for example, http://www.nda.

ac.jp/cs/AI/wehia04.

2. I have listed the references to several important models. Early research

and recent working papers on the agent-based modeling of financial

markets can be found on W. A. Brockâ€™s (http://www.ssc.wisc.edu/

$wbrock/),

C. Chiarellaâ€™s (http://www.business.uts.edu.au/finance/staff/carl.html),

J. D. Farmerâ€™s (http://www.santafe.edu/$jdf),

B. LeBaronâ€™s (http://people.brandeis.edu/$blebaron/index.htm),

T. Luxâ€™s (http://www.bwl.uni-kiel.de/vwlinstitute/gwrp/team/lux.htm), and

S. Solomonâ€™s (http://shum.huji.ac.il/$sorin/) websites.

3. In a more consistent yet computationally demanding formulation, the

function fi depends also on current return rt , that is, Ei , t[rtÃ¾1 ] Â¼

fi (rt , . . . , rtÃ€Li ) [8, 9].

4. Log price in the left-hand side of equation (12.3.7) may be a better choice

in order to avoid possible negative price values [12].

5. See also Section 7.1.

6. This model has some similarity with the mating dynamics model where

only agents of opposite sex interact and deactivate each other, at least

temporarily. In particular, this model could be used for describing at-

tendance of the singlesâ€™ clubs.

7. Equation (12.4.19) can be transformed into the Schrodinger equation

with the Morse-type potential [19].

8. Another interesting example of qualitative difference between the con-

tinuous and discrete evolutions of the same system is given in [20].

References

CHAPTER 1

1. J. Y. Campbell, A. W. Lo, and A. C. MacKinlay, The Econometrics of

Financial Markets, Princeton University Press, 1997.

2. W. H. Green, Econometric Analysis, Prentice Hall, 1998.

3. S. R. Pliska, Introduction to Mathematical Finance: Discrete Time

Models, Blackwell, 1997.

4. S. M. Ross, Elementary Introduction to Mathematical Finance: Options

and Other Topics, Cambridge University Press, 2002.

5. R. N. Mantegna and H. E. Stanley, An Introduction in Econophysics: Cor-

relations and Complexity in Finance, Cambridge University Press, 2000.

6. J. P. Bouchaud and M. Potters, Theory of Financial Risks: From Statis-

tical Physics to Risk Management, Cambridge University Press, 2000.

7. M. Levy, H. Levy, and S. Solomon, The Microscopic Simulation of

Financial Markets: From Investor Behavior to Market Phenomena, Aca-

demic Press, 2000.

8. K. Ilinski, Physics of Finance: Gauge Modeling in Non-Equilibrium

Pricing, Wiley, 2001.

9. J. Voit, Statistical Mechanics of Financial Markets, Springer, 2003.

10. D. Sornette, Why Stock Markets Crash: Critical Events in Complex

Financial Systems, Princeton University Press, 2003.

11. S. Da Silva (Ed), The Physics of the Open Economy, Nova Science, 2005.

12. B. LeBaron, â€˜â€˜Agent-Based Computational Finance: Suggested Read-

ings and Early Research,â€™â€™ Journal of Economic Dynamics and Control

24, 679â€“702 (2000).

149

150 References

13. M. Jackson and M. Staunton, Advanced Modeling in Finance Using

Excel and VBA, Wiley, 2001.

CHAPTER 2

1. C. Alexander, Market Models: A Guide to Financial Data Analysis,

Wiley, 2001.

2. M. M. Dacorogna, R. Gencay, U. Muller, R. B. Olsen, and O. V. Pictet,

An Introduction to High-Frequency Finance, Academic Press, 2001.

3. See [1.1].

4. T. Lux and D. Sornette: â€˜â€˜On Rational Bubbles and Fat Tails,â€™â€™ Journal

of Money, Credit, and Banking 34, 589-610 (2002).

5. R. C. Merton, Continuous Time Finance, Blackwell, 1990.

6. Z. Bodie and R. C. Merton, Finance, Prentice Hall, 1998.

7. R. Edwards and J. Magee, Technical Analysis of Stock Trends, 8th Ed.,

AMACOM, 2001.

8. S. Cottle, R. F. Murray, and F. E. Block, Security Analysis, McGraw-

Hill, 1988.

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