تقدير القيمة المعرضة للمخاطر

//___________________ _____________//

)*(

--

Sarmad_aljamil53@yahoo.com

-

.

.

)* ( " " –

][/)(

The Estimation of Value at Risk in Arab Capital Markets by UsingArtificial Neural Networks / ANN

Sarmad K. Jameel (PhD)Assistant Professor

Department of Financial and BankingSciences

University of Mosul

Hasan S. Al – AbbasLecturer

Department of Business AdministrationAl - Hadbaa University College

Abstract

The notion of value at risk has been seen as a method that can be broken down todemonstrate the facets of the risks in the business institutions especially the fanatical ones.The value at risk can generally be manipulated as an accurate module to estimate the worstloss expected through the temporal range founded under the market natural conditions onthe one hand and the identified level of trust on the other.

The current study is subjected to the real financial notifications by markets. Thegenerative notifications were from 1998 to the 12th of 2002 that represented 60 notificationallocated to the revenues, the market prices and the merchant period and the artificialneural networks (ANN) has been used in order to testing hypothesis.The most prominent results of the study are the difficulty to integrate the concepts ofvalue and risk management that can never be true in all circumstances. This can be

reflected to the formulation of decision-making process under the risk conditions.

.

-.

.

...][

.

..

.

-

) (

.

-:

.

..

.

][/)(

.

.-

.. :

.. ) ( :

) (

)VaR ( ) (

) ( (cdf)

)VaR. (

. : :

) (

.. :

)J.P.Morgan ()Basle( .

- :

...][

.

-

% )

( .

.

-

:

. :

=

. :

=

. .

. )( )VaR (

:

1-N)xx( i∑ −

=σ ......................................................................... ( )

–

][/)(

. :

• .• .• .•Sin .•A Sin .

. )Skewness( :

N

x x)-x(Y

33i^ ∑ ÷

=

Nσ

.................................................................. ( )

. )Kurtosis( :

N

x x)-x(Y

44i^ ∑ ÷

=

Nσ

..................................................................( )

. (cdf) )VaR( :

(N))P(Fcdf ∆= ............................................................................. )(

. )VaR ( )/( :

[ ] [ ]TVaRVaR **P-P-VaR 1/2TPp ρασα === ∑ww ................ )(

.)VaR ( (ConditionalProbability Function / cpf(:

∫∞

=∆==-Var

c-1dx(x))P(PrVaR f ....................................................( )

. )VaR ()–( :

dtdS21dSVaRdP 2 Θ+Γ+∆== .................................................( )

...][

oSVaR σα×∆= ..........................................................................( )

. )VaR ( ) –( :

2dS21dSVaRdP Γ+∆== ..............................................................( )

2dyCV21DPdydP += ................................................................ ( )

. :

•.•

.•

.• ) (

%.. C++

)Hidden Nodes(

:(Eric&Patrick,1999, 16)(JackM.Zurada,1996, 22-27)

) (.........................) w*Iseg(XX0 iii +=:

X0i :.Xi :.

I :.wi :.

:

[ ] [ ][ ]

= ∑

=

N

0iiJw*iX0segOL(J) .................................................... )(

:J :.

N :.:

][/)(

= ∑

=

50

1iwo*i)OL(J,segO i .......................................................... )(

:i)OL(1,*Z*WO η= ............................................................ )(

:η :.

OL :.WO :.

Z ::D(out)seg*O-OdZ = ............................................................ )(

:Od :.

O :.segD :Sigmoid.

:OOde −= ............................................................ )(

:)segD(OL*WO*OL i2,Ii2, Z= ................................................... )(

i2,i1,iJJi, OL*OL* WW η+= ....................................................... )(

)segD(OL*W*OLOL i1,Ji,

2

1j2,i1, ∑

=

=J

.......................................... )(

i1,i OL* WIWI η+= ............................................................ )(

-

)VaR ((Rachev & Khindanova, 2002, 8) )VaR ( : ) (

) (

)(Sauders & Manfredo, 1999, 13

...][

)J.P. Morgan ()Risk Metrics (

)VaR ( )VaR (

)Linsmeier & Pearson, 1999, 35( . )VaR (

)Basle (

)VaR ( )Rachev & Khindanova, 2002, 8. (

)VaR (

)Basle (

)VaR (

(Rachev & Khindanova, 2002, 40).

-

)Ordering Risk (

.

][/)(

)Group of Thirty, 1993, 3. (

(Capital Asset Price Model / CAPM)

)CAPM ( )Beta(

(Golub & Tilman, 2000, 12) .Modern Portfolio Theory

)CAPM (): ()R-(ERBiRE(ri) FMF += ........................................... )(

:E(ri) :.

R F :.Bi :i.

MER :. ) (

)VaR (

)Delta ( )Theta ( )Vega ( )Rho(

)Pritsker, 1997, 14( .

)Offsetting (

). (

...][

)Malkiel & Xu, 1997, 3 :(• :

.• :

)Line of–Credit(

.

• : .

•: .

)VaR (

(Risk Adjusted Return on Capital/RAROC) :) (•

.•

.•

.•

(Market Value Simulation Models)

)VaR (

][/)(

)Market Value Stress Test (

(Fallon, 1996,6).

-

)Dollars-at-Risk /DaR(

(Capital-at-Risk/CaR) )Income-at-Risk/ IaR( (Earnings-at-Risk/EaR)

(Value at Risk/VaR) ) ( )DaR (

)CaR ( )IaR (

)EaR (

)Glyn, 2002, 24(.

(Marshall & Siegel, 1997, 3)

:•

)Venkatarman, 1997, 6( .

•

(Mathematical Functions) )Bennett,1997,51-55(.

•

)Yamada, 2001, 4.(

...][

• )Tasi, 2004, 5(.

% )VaR (

% % %

.

(Rachev & Khindanova, 2002, 3).

-)VaR ( :

•Parametric Framework : :/ Variance/Covariance Model

Approximations ModelQuadratic.•) (Non-Parametric Framework :

:Historical Simulation Model

Monte Carlo Simulation Model .•Artificial Neural Networks ANN

)VaR (

)J.P. Morgan ( (Linsmeier &

Pearson, 2000, 20) .

)Liu, 1996,

13( .)VaR (:

][/)(

.)VaR (

)

()Duffie & Pan, 1997, 34( . )VaR ( "

)C (% )D ( )N ( " )D ( :

)N ()C.(

)N( )(%

)VaR ( % )Studer, 1995, 6. (

Source: Studer, A., (1995), ETHZ, Value at Risk and Maximum Loss Optimization,Technical Report, Working Paper, 8.

VaR 0

99%

...][

)VaR ( %

% )VaR ( )((*)

) ()Studer, 1995, 6 .(

)VaR ( )Studer, 1995, 8-12: (

[ ] c-1-VaRp(N)pr =<∆ ………………………………………… )(:

c :.)N(pp(N) t∆=∆ : )P&L (

)N( .N).P(tP-N)p(t(N)P tt ++=∆ :

Nt + .tP :)t. (

ConditionalProbability Function (cpf) Conditional

Characteristics Function (ccf) )VaR(

)P&L(:

[ ] [ ] -cVaRPF 1d))P(()(-VaRp(N)PrVaR-VaR

-

=∆∫=−∆=<∆= ∫∞

χχ ... )(

:[ ](.)PF ∆ : ) ( )cdf (

)Cumulative Distribution Function.((.))(, PandP ∆∫∆ : )pdf (

)Probability Density Function(..

)VaR (

)VaR ( )VaR ( )VaR (

(*)) (Sigma.

][/)(

)(%)Bai, 2003, 10: (

tradedVaRVaRVaR day1month1 day== ........................... )(

)VaR ( :Month1 weeks2day1 VaRVaRVaR <<

)VaR) (Bai, 2003, 17. (

Source: Liu,Guochun,(2004),Value at Risk Models for a Nonlinear Hedged Portfolio, M.Sc. Thesis, Faculty of Worcester Polytechnic Institute, P. 12.

VaR

...][

-

(Liu,2004,12).

Source: Liu,Guochun,(2004),Value at Risk Models for a Nonlinear Hedged Portfolio, M.Sc. Thesis, Faculty of Worcester Polytechnic Institute, P. 12.

)VaR(

)VaR (

) (

VaR

][/)(

)VaR ()Liu,2004, 16. (

. Supervised Learning

(Back PropagationNeural Network)

NodeHidden

). (

.

(MSE =0.01%)

:

Node

) (

-.

...][

Learning RateTime Learning Rate (minute)Error Rate

020406080

100

1 7 13 19 25 31 37 43 49 55 610

102030405060

1 5 9 13 17 21 25 29 33 37 41

][/)(

050

100150200250

1 8 15 22 29 36 43 50 57 64 71 78 850

50100150200250300

1 6 11 16 21 26 31 36 41 46 51 56

050

100150200250300

1 6 11 16 21 26 31 36 41 46 51 56 61

0

50

100

150

1 4 7 10 13 16 19 22 25 28 31 34

...][

)Node (

)Node (

%

)VaR( :

/

cpf

050

100150200250300

1 6 11 16 21 26 31 36 41 46 51 56 61

0

50

100

150

1 4 7 10 13 16 19 22 25 28 31 34

][/)(

)VaR (

VaR VaR VaR VaR VaR VaR

/

/

cpf

cpf

/

/

cpf

cpf

/

/

cpf

cpf

/

/

cpf

...][

cpf

/

/

cpf

cpf

/

/

cpf

cpf

/

/

cpf

cpf

/

/

cpf

cpf

][/)(

)ANN ( )VaR (:

ANN

) – (

) – ( )cpf ( /

)– (

.

ANN

-

-

)cpf (

/

.

...][

)cpf ( )VaR (

)VaR ( )cpf (.

% :

. ) – (

..

.

)Skewness (

)Kurtosis (

) Sinasin(

.

][/)(

.

.. ) (

) (

.. )VaR (

(cdf)

.

Basle

.

.

-. )ECMA(

htm.6brochures/Arabic/eg.org.aecm.www..).(

...][

.Bruce Lierman ..

.Dennis Bennett/ .

.Joseph & Chris MillsTeplitz .

. .

.

..)www.as.com.tadawul (.)www.msm.gov.com (

.)www.kuwaitse.com/defauit.aspx( .)www.ase.com.jo/ar/index.php( .)www.egyptse.com/main-a-asp( .)www.bumt.com.as ( .)www.casablanca.bourse.com/. ( .)www.amf.org.ae/vArabic( .)www.isx-iq.net(

- 1. Ahmad A.,Estimation of Value At Risk, Submitted to the Graduate Faculty of the

University of New Orleans .2003.2. Andreas, de vries, The value at risk, www.ruhr-bochun.de .2000.3. Andrey, Ragachev, Dynamic Value at Risk, Working Paper,

www.gloriamundi.org/picsresources/ardv .1999.4. Arnold, Glen, Corporate financial management, prentice-Hall, England.1998.5. Bai Bo,Value at Risk, National University of Singapore Science Drive 2, Singapore.

2003.6. Bouwman, M. J. & Frishkoff, how do financial analysis make decisions?, Accounting

organization society.1998.7. Dowd, K.,Beyond value-at-risk : the new science of risk management, John Wiley &

Sons.1998.8. Duffie, D. & Pan J., An overview of value at risk, journal of derivatives, No.4. 1997.9. Eric D. & Patrick N. Neural Networks, Macmillan,1995.10. Fallon, W.,Calculating Value at Risk, Wharton Financial Institutions Center, Working

Paper , 1996.11. Fama E. F. & French F., Risk Factors The Return On Stock Bond,Journal of Financial

Economics,Vol .33, No.1.1993.12. Glyn A. Holton, History of Value-at-Risk:1922-1998, Working Paper,

http://www.contingencyanalysis.com, 2002.13. Glyn, Holton A.,Simulation value at risk, journal of risk, No.11.1998.14. Golub, B., & Tilman,L., Risk Management: Approaches for Fixed Income Markets,

John Wiley and Sons, Inc.2000.

][/)(

15. Group of Thirty, derivatives: practices and principles, Global derivatives studygroup.1993.

16. Grundy, B. D. & Wiener, Z., The analysis of VaR: delta and state price: A newapproach, Working Paper, Rodney L. white Center for financial research the WhartonSchool, 1996.

17. Jack M.Zurada, Introduction to artificial neural systems , Jacio Publishing House. 1996.18. Linsmeier, Thoms & Pearson, Neil, Risk measurement : An Introduction to value at

risk, financial analysis journal, No. 56, MAR/APR.2000.19. Linsmeier, Thoms & Pearson, Neil, Risk measurement : An Introduction to value at

risk, financial analysis journal, No. 56, MAR/APR.2000.20. Liu, R., VaR & VaR derivatives, Capital market strategic, September.1996.21. Liu,Guochun,Value at Risk Models for a Nonlinear Hedged Portfolio, M. Sc. Thesis,

Faculty of Worcester Polytechnic Institute .2004.22. Lyman O. T., An Introduction to Statistical Method and Data Analysis, 3rd Ed., PWS,

KENT.1988.23. Malkiel B. G. & y. Xu, Risk And Return Revisited , Journal Portfolio Management ,

Vol. 23, No. 3 .01997.24. Marshall, C.,&, Siegel,M., Value at Risk : Implementing A Risk Management Standard,

Journal of Derivatives,Vol.4 .1997.25. Marshall, C.,&, Siegel,M., Value at Risk : Implementing A Risk Management Standard,

Journal of Derivatives,Vol.4 .1997.26. Miroslav Holecy, Application of Neural-Fuzzy Systems in Financial Management,

Masters Thesis Laboratory of Artificial Intelligence, Technical University of Ko¹ice,,16 , 2003 .

27. Pritsker, M., Evaluating value at risk methodologies, Journal of financial servicesresearch, 12:2/3.1997.

28. Rachev, S., E. Schwartz, & Khindanova, I., Stable Modeling of Market and CreditValue at Risk, Working Paper.2002

29. Rachev, S., E. Schwartz, & Khindanova, I., Stable Modeling of Market and CreditValue at Risk, Working Paper.2002

30. Sauders, Dwight R. & Manfredo, Mark R., Corporate risk management and the role ofvalue at risk, working paper, Arizona s 1999.

31. Studer, A., ETHZ, Value at risk and maximum loss optimization, Technical report,working paper. 1995.

32. Tasi, Kao-Tai, Risk Management Via Value At Risk, A ventis pharmaceuticalsbridgewater, New Jersey, USA. 2004.

33. Venkatarman, S., Value at risk for A mixture of normal distributions: the use of quasiestimation techniques, federal reserve bank of Chicago economic perspectives .1997.

34. Yamada, Yuji, Value-at-Risk Estimation For Dynamic Hedging, International Journalof Theoretical and Applied Finance Vol. 5, No. 4.2001.