تقدير القيمة المعرضة للمخاطر

28
ÞNë¢Ë¦× ìÜàN ~ ©© ¯ ° Œ ţƒŧœř ƅƄŪřƃ ÎÓ / Î / ÏÍÍÔ ___________________ _____________ ŧŬƈƃŒ ¾ƍŕſ ţƒŧœř Ó / Ò / ÏÍÍÔ ŧűœŤƆƄƃ ŗŰŧŶƆƃŒ ŗƆƒƀƃŒ ŧƒťƀř ŗƒŕŧŶƃŒ ŗƒƃœƆƃŒ žŒŧƍƕŒ žŒƍŪƕ ƅŒťŤřŪœŕ ŗƒŵœƈűŮƙŒ ŗƒŕŮŶƃŒ ŘœƂŕŬƃŒ ) * ( ¾ƒƆŞƃŒ ŔƂƍƂ ťƆŧŪ ŧƍřƂťƃŒ ŧŷŕŬƈ ŨŕśŬŌ - řƔžũŰƈƅŔƏ řƔƅŕƈƅŔ ƇƏƆŸƅŔ ƇŬƁ ŧŕŰśƁƛŔƏ ŘũŔŧƙŔ řƔƆƄ - ¿ŰƏƈƅŔ řŸƈ੠[email protected] ƇŪš ƑšŕŮ ƇŪš ūũŧƈ - ƔƆƄ řŸƈŕŠƅŔ ʼnŕŗŧţƅŔ ř ŭƄŤřŪƆƃŒ Δ ϤϴϘϟ ϦϴϣΎπѧϣ Ϧ ϋ ϒθѧϜϟ Ϯ Τϧ ˱ΎѧϴϘϴΒτΗϭ ˱ Ύ ϳήψϧ ΔѧϴϟΎϤϟ ΓέΩϹ ϲ ϓ ΕΎѧγέΪϟ ΖѧϬΠΗ Δѧϴϓήόϣ ΔϠϴμѧΣ ΎϬϔѧλϮΑ ήσΎΨϤϠϟ ΔοήόϤϟ ΔϤϴϘϟ ΝΫΎϤϧ ΖϤϫΎγ Ϊϗϭ ˬήσΎΨϤϠϟ ΎϬοήόΗ ϯΪϣϭ Ϸ έΎό γ ΎѧϬϟ νή όΘΗ Ϊ ϗϲ Θϟ ήΎδ Ψϟ ϰѧϠϋ ϑϮϗϮϟΎ Α ϩΎ ΠΗϻ ά ϫ ΕήѧΛ ϲ ϓ ΎϬΗή ηΆϣϭ ϢϬ γ ΚΤΒϟ ΔϴϤϫ ϞΜϤΘΗ ˬΔϴϟΎϤϟ ϕέϭϷ ϕϮγ ϲϓ ΔѧοήόϤϟ ΔѧϤϴϘϟ ΞϫΎѧϨϣ ϞѧϤϋ Δѧϴϟ ϰѧϠϋ ϑήόΘϟ ˬΎѧϬΗΎϴΜϴΣ ϥΎѧϴΑϭ ΔѧϴϟΎϤϟ ΕΎѧϧΎϴϜϟ ΎѧϬϟ νήѧόΘΗ ϲѧΘϟ ΔѧϠϤΘΤϤϟ ήΎδѧΨϟ ήϳΪѧϘΗ ϲѧϓ ΓΩ΄ϛ ήσΎΨϤϠϟ Ϩѧϳ ΎѧϤΑϭ ήσΎѧΨϤϟ Ϟѧχ ϲѧϓ ΔѧϤϴϘϠϟ ΔϘϴϗΩ ΕήϳΪϘΗ ϰϟ· ϝϮλϮϠϟ ΚΤΒϟ ϑΪϬϳϭ ςϴѧτΨΘϟ ϰѧϠϋ βϜό ΩϮѧΟϮΑ Δѧϗϼόϟ ΕΫ ϑήѧσϷ ϯΪѧϟ έήѧϘϟ ΫΎѧΨΗ ΔϴϠϤϋ ϢϋΪϳ ϱάϟ ϞϜθϟΎΑ ΞΎΘϨϟ αΎϴϗϭ ˯ΩϷϭ ΔϴϟΎϤϟ ΔδγΆϤϟ . ΐδѧΤΘϟ ΎϬϓΪѧϫ ΔϨϳΎΒΘϣ ΕϭΩϭ ΝΫΎϤϧϭ ΞϫΎϨϣ ϦϤο ϦϴΜΣΎΒϟ ΩϮϬΟ ϚϟΫ ϲϓ ΕΩΪόΗ ΪϘϟ ΔϴΒϠδѧϟ ΎѧϫέΎΛ ξϔΧϭ ΓήσΎΨϤϟ ΙϭΪΤϟ ΔϨϜϤϤϟ ΕϻΎϤΘΣϻ ϞϜϟ ΔϴѧγΎγϷ Δϴѧοήϔϟ ΪѧϳΪΤΗ ϢѧΗϭ ΕϻϭΪѧΗ ϪѧΟϮΗ Ϊѧϗ ϲѧΘϟ ΔϠϤΘΤϤϟ ήΎδΨϟϭ ήσΎΨϤϠϟ ΔοήόϤϟ ΔϤϴϘϟ ήϳΪϘΗ ΔϴϧΎϜϣ· ϲϓ ΔγέΪϠϟ ΕΪѧϤΘϋϭ έΎϤΜΘѧγϻ ρΎθѧϧ ϪѧΟϮΗ Ϊѧϗ ϲѧΘϟ ήΎδѧΨϟ έΪѧϘϣ ϰϟ· ϝϮλϮϟ ϲϓ ˬΎϬΗήηΆϣϭ ϢϬγϷ ϣ ϥΎѧϛϭ ΔϴοΎϳήϟϭ ΔϴΎμΣϹ ΐϴϟΎγϷ Ϧϣ ΔϋϮϤΠϣ ϰϠϋ ΔγέΪϟ ϞѧϴόϔΗ ΔѧϴϧΎϜϣ ΎѧϬΠΎΘϧ Ϣѧϫ Ϧ ϰϠϋ ΪϋΎδΗ βγ ϲϨΒΗϭ Δϗϼόϟ ΕΫ ϑήσϷ ήϜϓ ήϳϮτΗ ϲϓ ϢϬδΗ ΓΩ΄ϛ ήτΨϠϟ ΔοήόϤϟ ΔϤϴϘϟ ΔϴϟΎϤϟ φϓΎΤϤϟ ˯ΎϨΑ . ) * ( ƋŔũƏśƄŧƅŔ řţƏũųŌ Ɖƈ ¿śŬƈ ŜţŗƅŔ řƈƏŬƏƈƅŔ " ʼnŕ»Ɗŗ Ɠ»ž ũųŦƆƅ řŲũŸƈƅŔ řƈƔƂƅŔ ƇŔŧŦśŬŔ řƔŗũŸƅŔ řƔƅŕƈƅŔ ƀŔƏŬƗŔ Ɖƈ ŧŧŸƅ řƔƅŕƈƅŔ ƀŔũƏƗŔ Ŵžŕţƈ " ŧŕŰśƁƛŔƏ ŘũŔŧƙŔ řƔƆƄ ř»Ÿƈ੠¿ŰƏƈƅŔ

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Page 1: تقدير القيمة المعرضة للمخاطر

//___________________ _____________//

)*(

--

[email protected]

-

.

.

)* ( " " –

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][/)(

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.

.

-.

.

Page 3: تقدير القيمة المعرضة للمخاطر

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.

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) (

.

-:

.

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Page 4: تقدير القيمة المعرضة للمخاطر

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.

.-

.. :

.. ) ( :

) (

)VaR ( ) (

) ( (cdf)

)VaR. (

. : :

) (

.. :

)J.P.Morgan ()Basle( .

- :

Page 5: تقدير القيمة المعرضة للمخاطر

...][

.

-

% )

( .

.

-

:

. :

=

. :

=

. .

. )( )VaR (

:

1-N)xx( i∑ −

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

Page 6: تقدير القيمة المعرضة للمخاطر

][/)(

. :

• .• .• .•Sin .•A Sin .

. )Skewness( :

N

x x)-x(Y

33i^ ∑ ÷

=

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

. )Kurtosis( :

N

x x)-x(Y

44i^ ∑ ÷

=

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

. (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+∆== .................................................( )

Page 7: تقدير القيمة المعرضة للمخاطر

...][

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 :.:

Page 8: تقدير القيمة المعرضة للمخاطر

][/)(

= ∑

=

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

Page 9: تقدير القيمة المعرضة للمخاطر

...][

)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 (

.

Page 10: تقدير القيمة المعرضة للمخاطر

][/)(

)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 (

). (

Page 11: تقدير القيمة المعرضة للمخاطر

...][

)Malkiel & Xu, 1997, 3 :(• :

.• :

)Line of–Credit(

.

• : .

•: .

)VaR (

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

.•

.•

.•

(Market Value Simulation Models)

)VaR (

Page 12: تقدير القيمة المعرضة للمخاطر

][/)(

)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.(

Page 13: تقدير القيمة المعرضة للمخاطر

...][

• )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 (:

Page 14: تقدير القيمة المعرضة للمخاطر

][/)(

.)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%

Page 15: تقدير القيمة المعرضة للمخاطر

...][

)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.

Page 16: تقدير القيمة المعرضة للمخاطر

][/)(

)(%)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

Page 17: تقدير القيمة المعرضة للمخاطر

...][

-

(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

Page 18: تقدير القيمة المعرضة للمخاطر

][/)(

)VaR ()Liu,2004, 16. (

. Supervised Learning

(Back PropagationNeural Network)

NodeHidden

). (

.

(MSE =0.01%)

:

Node

) (

-.

Page 19: تقدير القيمة المعرضة للمخاطر

...][

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

Page 20: تقدير القيمة المعرضة للمخاطر

][/)(

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

Page 21: تقدير القيمة المعرضة للمخاطر

...][

)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

Page 22: تقدير القيمة المعرضة للمخاطر

][/)(

)VaR (

VaR VaR VaR VaR VaR VaR

/

/

cpf

cpf

/

/

cpf

cpf

/

/

cpf

cpf

/

/

cpf

Page 23: تقدير القيمة المعرضة للمخاطر

...][

cpf

/

/

cpf

cpf

/

/

cpf

cpf

/

/

cpf

cpf

/

/

cpf

cpf

Page 24: تقدير القيمة المعرضة للمخاطر

][/)(

)ANN ( )VaR (:

ANN

) – (

) – ( )cpf ( /

)– (

.

ANN

-

-

)cpf (

/

.

Page 25: تقدير القيمة المعرضة للمخاطر

...][

)cpf ( )VaR (

)VaR ( )cpf (.

% :

. ) – (

..

.

)Skewness (

)Kurtosis (

) Sinasin(

.

Page 26: تقدير القيمة المعرضة للمخاطر

][/)(

.

.. ) (

) (

.. )VaR (

(cdf)

.

Basle

.

.

-. )ECMA(

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

Page 27: تقدير القيمة المعرضة للمخاطر

...][

.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.

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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.