2  1   1 13  4     3 2 1 2

(1)

2008 / 2009

(2)

1

2

(3)

2 1 2

3 



4 



(4)

5 Fama

.

(5)

Fair Game

لولأا عرفلا :

يلاملا قىسلا مىهفم .

1N. G. MANKIW: « Principles of Macroeconomics , Mc Gro w Hill, New Yo rk, 3^rd edition, 2003, P267 .

2 F. S. MISHKIN : «The Econo mics of Money, Banking, and Financia l Markets , 7^th edition, Pea rson Addison Wesley, New York, 2004, P23.

(6)

«

Lequidity

Search Costs

Information Costs Explicit Costs

Implicit Costs

Maturity of the claim

1 S. A. ROSS et al : «Funda mentals of Co rporate Finance , The Mc Grow Hill co mpanies, New York, 6^th edition, 2002, P50.

2 J. F. FABOZZI et a l. : Handbook of Financial Instruments , John Wiley & Sons, Ne w Je rsey, 2002, P8-9.

(7)

1.1 Financial Market

Money Market Capital Market

¹

1.1 .

1 1

1999 7

long-Term Debt Instruments Original Maturity

Equity Instruments Risks

3

1

يبٌّا طأس قٛع شجزو٠ ش١خلأا از٘ ش١د ،حلاـطلاا خ١دبٔ ِٓ ٟغٔشفٌا ُ١غمزٌا ٓه فٍزخ٠ ٞزٌا قٛغٌٍ ٟٔٛغوبعٍٛجٔلأا ُ١غمزٌا بٕ١ٕجر قدلاِ ٛ٘ بّو 1

Marché de Capiteau x ذمٌٕا قٛع ٗزذر ُؼ٠ ٞزٌا ٛ٘

Marché Monétaire ٌٟبٌّا قٛغٌاٚ

Marché Financier .

2 F. S. MISHKIN: The Econo mics of Money, Banking, and Financia l Markets , 7^th edition, Pearson Addison Wesley, New York, 2004, P27.

3 B. S. KALISKI et al: Encyclopedia of Business and Finance V: I , Mac millan Reference USA, Ne w Yo rk, 2001, P85.

(8)

2 3 4

1 Debt Markets or Bond Markets

2 Equity Markets or Stock Markets

Primary

Market Secondary Market

1 Investment Bank

Commercial Bank

يٚأ قٛع ٌٝإ قٛغٌا ُغم٠ ٞزٌا هٌر نِ ُ١غمزٌا از٘ ؾٍخ٠ لا ْأ تج٠1

First Market

ٍْبص قٛعٚ

Second Market –

قٛغٌا ٟف يبذٌا ٗ١ٍه ٛ٘ بّو

ٟغٔشفٌا -

، ٖز٘ ٍٓىّ٠ ش١د ٍٟئبوٌا نثبـٌا دارٚ ش١غظٌا ُجذٌا دار دبوششٌ ضظخِ ٟٔبضٌا بّٕ١ث ش١جىٌا ُجذٌا دار دبوششٌٍ بًظظخِ يٚلأا ْٛى٠ ش١د

حشـ١غٌا ْاذمف شؿبخِ ِٓ غفخٌا ِٓ حش١خلأا Control

ًلأ ؽٚششٚ ف١ٌبىزث قٛغٌٍ يٛخذٌا ِٓ خغعؤٌّا ٓىّ٠ بّو ؛ .

2 H. de VAULPANE et J.P. BORNET : Dro it des Marchés Financiers , Litec, Pa ris,1998, P318.

1997 3

8 9

(9)

2 Organized Securities Market

.Unorganized Securities Market

Multilateral 10

93 COSOB

²

SGBV

³

1 2 3

1 H. De VAULPANE et J.P. BORNET : Dro it des Marchés Financiers , Litec, Pa ris,1998, P321 .

2 COSOB : La Co mmission d’Organisation et de Surveillance des Opérations de Bourse.

3 SGBV : La Société de Gestion de la Bourse des Valeurs.

4 COSOB : Guide de l’Ad mission , ANEP, Alger,1997, P27-28.

َبلٔ 5

03 97

199 7

(10)

4 300

5 100

6 1 100.000.000

2 20

%

3 4 5 6 7 8

Bilateral

1 2 COSOB : op. c it, P42.

(11)

.

1 03

2 Futurs Markets

1 H. de VA ULPA NE et J.P. BORNET : op. c it, P330.

ِٓ ُغمٌا از٘ ٟف ُ١غمزٌا از٘ تٕجر ًؼفلأا ِٓ ٗٔأ بٕ٠أس ش١د ،بٙ١ف خٌٚاذزٌّا خ١ٌبٌّا دبجزٌّٕا تغد ٜشخأ خ١هشف قاٛعأ ٌٝإ قٛغٌا از٘ ُغم٠ ِٓ نبٕ٘2

خ١ٌبٌّا داٚدلأٌ ضظخٌّا ءضجٌا ٟف بًمدلا ٗ١ٌإ قشـزٌا ُز١ع ٗٔلأ ،شذجٌا .

(12)

IFRS

²

01 597 96

02 1996

1 2 3 4 6

546 98

1 H. de VAULPANE et J.P. BORNET : op. c it, P36-37.

2 IFRS : International Financial Reporting Standards.

3 P. BA RNITO, P. GRUSON : Instruments Financiers et IFRS »,DUNOD, Paris, 2007, P13.

4 La lo i de Modernisation des Activités Financières.) MAF(

5 Les Va leurs Mobilières.

6 BMTN : Bons à Moyen Terme Négociables.

(13)

1

2 1 Common Stock

715 40

Book Value

خٍّو شور ُر ارإ ٗٔئف تٌبغٌا ٛ٘ خّ٘بغٌّا داذٕع ِٓ مٌٕٛا از٘ ْأ سبجزهبث 1

«

ُٙع »

ٛ٘ دٛظمٌّا ْئف مٌٕٛا ذ٠ذذر ْٚد

"

ٞدبوٌا ُٙغٌا ."

ٞذٕ٘ ُ١٘اشثا ش١ِٕ2

: 1999

7

خٍـظِ خ٠شزفذٌا خّ١مٌا ٍٝه كٍـ٠ ِٓ نبٕ٘ 3

: خٍـظٌّ خ١غٔشفٌا ٓه خّجشزٌا ِٓ بًللاـٔا هٌر ٚ خ١ػب٠شٌا خّ١مٌا « La Va leur Mathé matique »

.

حدبٌّا 4

سشىِ 715

ٞشئاضجٌا ٞسبجزٌا ْٛٔبمٌا ِٓ 50 .

5 COSOB : « Guide des Va leurs Mobiliè res », ANEP, Alger,1997, P10-12.

(14)



Prefered Stocks

1 COSOB: » Gu ide des Va leurs Mobilières », ANEP, A lger,1997, P13-14.

2 Les actions de jouissance.

(15)

Golden Share 133 96

05 »

1 Amort issement du capital.

2 ABSA : Les Actions à Bons de Souscription d’Actions.

3 L’ Action Spéc ifique.

فٛفذِ سبجج :

خطسٛجٌبث ف٠شوزٌا خٍغٍع –

ءضجٌا :2 صسٛجٌا ٟف خٌٚاذزٌّا خ١ٌبٌّا قاسٚلأا ح

،شئاضجٌا ،ِٗٛ٘ ساد ،

.2002 ⁴

5 P-J. LEHMANN : » Bourse et Marchés Financiers », Dunod, Paris, 2002, P21.

ٌٛا6

.

َ .أ : خ١ى٠شِلأا حذذزٌّا دب٠لاٌٛا .

(16)

1 Coupon

2 Floting Rate Bonds

3 Indexed Bonds

Stabilized Bonds

4 Zero Coupon Bonds

5 SICV

FCP

³

FCC

⁴

SCPI

⁵

فٛفذِ سبجج 1

: ص ،كثبغٌا نجشٌّا .58

2SICV: Sociétés d’Investissement à Capita l Variable.

3 FCP : Fonds Communs de Place ment.

4 FCC : Fonds Co mmuns de Créance.

5SCPI : Sociétés Civiles de Place ment Immob ilier .

(17)

عبارلا عرفلا :

ةيلاملا تاقتشملا .

1 Forwards

»

2 Swaps

3 Furures

4 Options

1

1 John Hull: « Option, Future et Autre Dérivés »-Traduit par : P. Rorger et al., Pea rson Education, France, 2004.

2P. BA RNITO, P. GRUSON op. c it,, P126 .

3 F. BLA CK & M. SCHOLES : « The Pricing of Option and Corporate Liabilities », The Journal o f Po lit ical Economy, V81, I3, May – Jun 1973, P673.

: 1999

57

(18)

»

1 COB

³

67 833

28 1967

SEC

⁴

MAF 1996

1J.M. Keynes : « Théorie Générale de l’e mplo i, de l’intérêt et de la monnaie » –Traduction de J. Largentaye–, Payot, Paris, 1982,P163.

2 J.M. Keynes :op. cit, P163.

3 COB: Co mmission des Opérations de Bourse.

4 SEC: Securities Exchange Co mmission.

(19)

67 833 28

1967



 نِ ددادصا ذلٚ خوعاٚ ٚذجر خٕجٌٍا ٖز٘ ٌٝإ خٍوٌّٛا َبٌّٙا ْإ MAF

1996

2 CMF

²

CBV

³

CMT

⁴

1996

16 2

6 3

3 يناثلا عرفلا :

يلاملا قىسلا يف نىلخدتملا .

- 1 MAF 1996

2 CM F: Conseil des Marchés Financiers.

3 CBV: Conseil de la Bourse de Va leurs.

4 CBV: Conseil du Marché à Termes.

ذّذِ ٞٚذث ٗؿ ذ١ع5

:

،خ١ثشوٌا خؼٌٕٙا ساد ،خ١ٔٛٔبمٌا خٙجٌٛا ِٓ خٍج٢اٚ خ٠سٛفٌا خ١ٌبٌّا قاسٚلأا خطسٛث دب١ٍّه ص،2001

-289 .290

(20)

- 2

ْٛ١غ١عؤزٌا ْٚشّضزغٌّا .

- 3

- 4 طأس نفسٚ

خ١جسبخ ً٠ّٛر خم٠شـو داذٕغٌا ساذطئث ٚأ بٌٙبِ

.

5 1 2 3 1

2 4 1

2

سبجج فٛفذِ 1

: ،ٖاسٛزود خٌبعس ،خ١ِّٛوٌا دبغعؤٌّا خظطٛخٚ ش١١غر ،ش١١غزٌا ،خطسٛجٌا ص ،1997

.291

(21)

3 5 1

2 1 2

.(t=0)

1

2G.E.PICHES: Essentials of financial management, 4^th edition,Happer Collins publisher, Ne w Yo rk, USA, 1992, P10.

(22)

.1 1

𝑃

₀

= 𝐶𝐹

_𝑛

1 + 𝑖

⁻¹

1.1

𝑛 =𝑡

𝑛 =0

P

₀

n=0

CF

_n

n

i t 0

𝑃

₀

= 𝐷

₁

1 + 𝑖 + 𝐷

₂

1 + 𝑖

²

+ ⋯ + 𝐷

_𝑛

1 + 𝑖

^𝑛

+ 𝑃

_𝑛

1 + 𝑖

^𝑛

2.1 𝐷

_𝑗

j

P

_n

n

𝑖

𝑃

₀

= 𝐷

_𝐽

1 + 𝑖

^𝐽

(3.1)

∞

𝐽 =1

1

(23)



1

1956 g

𝑃

₀

= 𝐷

₁

1 + 𝑖 + 1 + 𝑔 𝐷

₁

1 + 𝑖

²

+ ⋯ + 1 + 𝑔

^𝑛−1

𝐷

₁

1 + 𝑖

^𝑛

(4.1)

𝑃

₀

=

¹

1 + 𝑖 1 + 1 + 𝑔

1 + 𝑖 + ⋯ + 1 + 𝑔

^{𝑛 −1}

1 + 𝑖

^𝑛−1

(5.1) n

r=

_1+𝑖¹⁺

𝑃

₀

= 𝐷

₁

1 + 𝑖

1 − 1 + 𝑔 1 + 𝑖

𝑛

1 − 1 + 𝑔 1 + 𝑖

(6.1) n

 i

g (i>g)

1+𝑔 1 +𝑖

𝑛

0 n

: 𝑃

₀

= 𝐷

₁

𝑖 − 𝑔 (7.1) (7.1)

1 JL.VIVIANI:Gestion de portefeuille,2^e édit ion, Dunod, Paris, France,2001. P23-24.

(24)

 i

g (i  g) i  g

2 Bates

1962

2

PER

𝑃𝐸𝑅 =

(8.1)

PER PER

W. Sharp

1 JL.VIVIANI: op. c it, P28 .

2 PER: Price Earning Ratio.

3 SHA RPE Willia m F.: « Capita l Asset Prices A Theory of Market Equilibriu m under Conditions of Risk», The Journal of Finance, 19(3), 1964,PP425–442.

4 GOFFIN R. : » Principes de la Finance Moderne », 3^e édition, Econo mica , Pa ris, 2001,P19.

(25)

1 𝐸 𝑊 = 𝑊 𝑃𝑟 𝑊

+∞

−∞

(9.1) 𝐸 𝑊 =

^𝑛_𝑖=1

𝑊 𝑃𝑟

_𝑖

(10.1)

J. Bernoulli »

Petersburg Paradox

1

100.000

2

10.000 50.000 =

¹₂

×

0 +

¹

2

× 100.000

2 Von Newman & Morgenstern

 1

A B

B A

 2

A B

B C

A

C

 3

A B

3 0 100.000 0

10

(26)

X 30.000

0 100.000

1 2

0 000 100 0.5

000 0.5 30 1

30.000 𝑈 30 000 = 𝑈 0 × 0,5 + 𝑈 100 000 × 0,5

𝑈 30 000 = 0 × 0,5 + 10 × 0,5 𝑈 30 000 = 5

2.1 GOFFIN R. : « Principes de la Finance Moderne », 3

^e

édition, Economica, Paris, 2001,P23.

30.000 100.000

0 30.000 2.1

100.000

) ْٚ ( غٌبجٌّا خوفٌّٕا داششؤِ

10.000

- 7.5

30.000

2.5 5 10

10.000 -

(27)

3 3 𝑅 1

𝑅 = 𝑃

₁

+ 𝐷

₁

− 𝑃

₀

𝑃

₀

(11.1)

₁

/𝑃

₀

3 2 2.1

3 2

3 2 σ

_𝑤

ش١د ،َٛٙفٌّا از٘ خ١جغٔ ٌٝإ حسبشلإا سذجر 1

: ( )1 دشفٌٍ خوفٌّٕا خٌاد ًىش ْٛى٠ ْأ ٓىّ٠ رإ ذ١دٌٛا ًىشٌا ظ١ٌ خٌاذٌٍ ةذذٌّا ًىشٌا (

)2 بِّ ُ١مزغِ ؾخ

ْٛى٠ ْأ ٓىّ٠ بّو ،بٙ١ٌإ عشوز٠ ٟزٌا شؿبخٌّا خجسذث ِيبجِ ش١غ دشفٌا ْأ ٟٕو٠ (

)3 ُٙ٠ذٌ ٓ٠زٌا داشفلأا ضخر خٌبذٌا ٖز٘ٚ ذ٠اضزث حذ٠اضزِ ٞأ شومِ ٕٝذِٕ

حشِبغٌّا حٚس .

خج١زٔ خٌاذٌا ٖز٘ ْأ هٌر ٌٝإ فػأ

ةسبش حشىف ٍٝه اًءبٕث هٌرٚ ُ١١مزٌا خ١ٍّه ٟف بٌٙبخدإ ٚ شؿبخٌّا طب١ل ٓه حسٛط ءبـهإ ؾمف يٚبذٕع شذجٌا ِٓ ءضجٌا از٘ ٟف 2

W. SHA RP .

(28)

σ

_𝑤

> 0 2

𝑑𝑈/𝑑𝜎

_𝑤

< 0 Indifference Curves

1.3 3.1

HIRSHLEIFER J. : « Price Theory and Applications », 3

^e

edition, PH Inc., New Jersey, 1984,P74.

1 SHA RPE Willia m F.: « Capita l Asset Prices : A Theory of Market Equilibriu m under Conditions of Risk», The Journal of Finance,V 19 I(3), 1964.P428.

𝐸_𝑤

0 𝜎_𝑤

C D A B

(29)

1.3 A B C D

A

1 σ

_RF

= 0

0,𝐸

_𝑅

𝐸

_𝑅𝐹

F

4.1

4.1 SHARPE William F.: « Capital Asset Prices: a Theory of Market Equilibrium under Conditions of Risk», The Journal of Finance, 19 I(3), 1964.P432.

يلاخ ِٓ

σ

_R

≠ 0 4.1

F

A

يبّهلأا دآشِٕ ب٘سذظر ٟزٌا داذٕغٌٍ خجغٌٕبث خطبخ ،شؿبخٌّا خّ٠ذه داذٕغٌا ًو ذغ١ٌ 1

.

ِٓ ذوؤزٌا َذه خجسد ٗث دٛظمٌّاٚ بًّئاد ةسبش َٛٙفِ ٛ٘ قب١غٌا از٘ ٟف حدٛظمٌّا شؿبخٌّا بّٔإٚ ،كٍـٌّا ِٗٛٙفّث شؿبخٌّا ٕٝوِ ُٙف٠ ْأ تج٠ لا 2

نلٛزٌا ذئبوٌا .

B

Z

0 𝐸

_𝑅

σ

_R

C

Ø A

F

عشمِ

عشزمِ

(30)

F 𝛼 A

1 − 𝛼 A F

𝐸

_𝑅𝐼

𝐸

_𝑅𝐼

= 𝛼𝐸

_𝑅𝐹

+ 1 − 𝛼 𝐸

_𝑅𝐴

(15.1) :

F

A

σ

_RF

= 0 F

𝜎

_𝑅𝐼

= 1 − 𝛼 𝜎

_𝑅𝐴

(17.1) 1 − α A

% %

F 100

100 100 100

F 1 > 𝛼 > 0 A

Ø

% %

100 Ø

100 100 1 − 𝛼 F

100

(31)

𝛼 = 1 A Ø

F

% %

Ø 100 100

100 100

AZ 𝛼 > 1 A

(𝛼 − 1) Ø

%

100 Ø 100

100(𝛼 − 1) F

100𝛼 100𝛼

Security Market Line

1952 F

. Ø

3 Ø

Ø

𝐸

_R

σ

_R

𝑃

(11.1) (12.1)

𝑃

₀

R

4.1 Ø

Ø Ø

A B 𝑃 C

A B C A

B

C Capital Market Line

5.1

1

(32)

2 𝜎

_𝑅

, 𝐸

_𝑅

, 𝑟

5.1 SHARPE William F.: op. cit, P436.

5.1 A

𝜎

_𝑅𝐴

, 𝐸

_𝑅𝐴

A

B 𝛼 F

A Combination

3 M M

i g

6.1 i

M

M’

6.1 i

M

iMM’

M

ٓ٠سبّضزعلاا ٓ١ث طضٌّبث شّضزغٌّا َٛم٠ طٛمٌا از٘ ٓ٠ٛىزٌ1

ـث i α

ٚ ـث g ( -1 α ) ذٕه ، : i 𝛼 = 1 . ذٕه : g 𝛼 = 0 . ذوث g 𝛼 < 0 g’

Z

0 𝐸

_𝑅

σ

_R

B A C

F

(33)

𝐸

_𝑅𝑖

𝐸

_𝑅𝑖

= 𝐸

_𝑅𝐹

+ 𝐸

_𝑅𝑀

− 𝐸

_𝑅𝑖

𝛽

_𝑖

(18.1)

𝐸

_𝑅𝑖

i

𝐸

_𝑅𝐹

𝐸

_𝑅𝑀

𝛽

_𝑖

i

6.1 SHARPE William F.: op. cit,P437.

–CAPM– 18.1 Capital

i

ش٠ذمزٌا ذٕه ْٚشّضزغٌّا ٗش١و٠ ٞزٌا نػٌٛا ٓه خم١مد .

M’

Z

0 𝐸

_𝑅

σ

_R

i

M

F

(34)

𝛼

_𝑖 𝑖

𝜖

_𝑖

18.1 𝜎

_𝑅

𝑖

2

= 𝜎

_𝛽²_𝑖_𝑅_𝑀

+ 𝜎

_𝜖

𝑖

2

(20.1)

7.1 i

M

GOFFIN R. : op. cit, P81.

𝜎

_𝛽_𝑖_𝑅_𝑀

1 Systematic Risk 𝜎

_𝜖

2

𝑖

Non-Systematic Risk

𝜖

_𝑖𝑡

𝛽

_𝑖

𝑅

_𝑖𝑡

𝑅

_𝑀𝑡

𝛼

_𝑖

(35)

1 2

1 Fundamental Analyses

The interinsic

Value

2 Technical Analyses

»

«

1 Eugene F. FAMA: «Random Walks in Stock Ma rket Prices , Financial Analysts Journal, Jan-Feb 1995, P76.

(36)

1 2

3

4 25 30

20 03

06

1 J. L. Viv iani : op. c it, P238.

2 J.M. Keynes :op. cit, P166-170.

(37)

َٛ ١ٌا ي لا خ t+ 1 خج غ ٌٕب ث خ٠ ٛئ ٌّا .

5 »

Mouse Louis BACHELIER

1900

8.1 1990

2001

R. Brealey & S. Meyers : «Principles of Corporate Finance »,7

^th

edition, Mc Grow-Hill, New York, 2003, P350.

1 J.M. Keynes :op. cit, P169.

2 BA CHELIER, L. : « Théorie de la Spéculation », Annales scientifiques de l’E.N.S 3^e Sé rie, to me 17, France,1900, pp.21-86.

(38)

8.1 1990

2001

1 1828

Robert BROWN

Botanic scientist

Vermicular Motion

» Brownian Motion

2 1900

Louis BACHELIER

1900

1 L. BA CHELIER : « Théorie de la Spéculation », Annales Scientifiques de L’E.N.S 3^e série, to me 17, pp.21-86.

خ١ٍّوٌا خ٠دبوٌا خعسذٌٍّ خ١ٍّوٌا دب١ٌٛذٌا ٟف خدٚشؿلأا ٖز٘ دششٔ 2

Ecole Norma le Sientifique ENS نلٌّٛا ِٓ ً١ّذزٌٍ خٍثبل ٟ٘ٚ

:

http://www.nu mda m.org/

(39)

Théorie de la Spéculation 1

2 3

Fonction Symétrique

]-∞,+∞[

]-∞,0[

𝐸 𝑥 =

₀^+∞

𝑝 𝑥 𝑑𝑥 = 𝑘 𝑡 (21.1) x

p t k k

Coefficient d’instabilité Coefficient de nervosité

3 1953

Mauris KENDALL 22

Pattern Wondering Series

يبّزدلاٌ ٓ١ِٛٙفِ ٚأ ٓ١هٛٔ نبٕ٘ ٗ١١ٌٛشبجٌ خجغٌٕبث 1

: ٟف طسذ٠ ٞزٌا ٛ٘ ٚ بًمجغِ ٗ١ٌإ يٛطٌٛا ٓىٌّّا ِٓ ٞزٌا يبّزدلاا ٟٕو٠ يٚلأا قذٌا ةبوٌأ

Jeu x

au Hasard خ١ػب٠س خم٠شـث ٗث ؤجٕزٌا ٓىّ٠ لا ٌٟبزٌبثٚ ٍٟجمزغِ سذد ٍٝه فلٛزٌّا يبّزدلاا ٟٕو١ف ٟٔبضٌا بِأ ،

. يلاخ ِٓ طٚسذٌّا ٛ٘ ٟٔبضٌا از٘ ْبوٚ

ٗزدٚشؿأ .

ٟو١جـٌا ن٠صٛزٌا ٟف يبذٌا ٗ١ٍه ٛ٘ بّو ،ٟػب٠شٌا نلٛزٌٍ خجغٌٕبث اًشكبٕزِ بٙو٠صٛر ًىش ْٛى٠ ٟزٌا خٌاذٌا ٟ٘ حشكبٕزٌّا خ١ٌبّزدلاا خٌاذٌا 2

.

3 M. G. KENDA LL: The Analysis of Economic Time-Se ries—Pa rt I: Prices , Journal o f the Royal Statistical Society.

Series A (Genera l), 116(1), 11– 25.

𝑥

_𝑖+1

i+1

i

Demon of Chance

Economic Brownian Motion

4 1959

Harry Roberts levels Changes

Pattern Trend

Cumulation

Chance Model Holbrook

ْأ قدلا 1

ذداٚ مٛجعأ ٛ٘ ياذٕو خعاسد ٟف i .

ْٛ١عبعلأا ٍٍْٛذٌّا ٍّٗوزغ٠ ٞزٌا خٍـظٌّبث خٔسبمِ ش١جوزٌا از٘ ًّوزعا 2

: قٛغٌا حشوار .

(41)

يفناج 06 نم تعمج لكل قلاغلاا ثايىتسم :)12.1(لكشلا

.يعانصلا سنىجواد رشؤمل 1956 ربمسيد 1956-28 عىبسأ 52ـل قىسلا ثايىتسمل ةاكاحم :)10.1(لكشلا

Le ve l ي ىت سم لا Le ve l ي ىت سم لا

عىبسلأا عىبسلأا

)قلاغلاا راعسأ( تعمجلا ًلإ تعمجلا نم ثاريغتلا :)11.1(لكشلا

سنىجواد رشؤمل 1956 ربمسيد 28-1956 يفناج 06 نم عىبسأ 52ـل قىسلا ثاريغتل ةاكاحم :)9.1(لكشلا

Cha nge ر يغ تلا Cha nge ر يغ تلا

عىبسلأا عىبسلأا

H. V. ROBERTS: Stock-Market "Patterns" and Financial Analysis: Methodological Suggestions , Journal of Finance, 14(1), p. 4–6.

9 10

11

12

(42)

1 Runs

2 3

5 OSBORN

Diffusion Brown

Brownian Motion in the Stock Market

1964 NYSE

ٞأ داش١غزٌا دبوثشِ ؾعٛزِ 1

𝐸 𝑢_𝑡² 𝑢_t= 𝑃(𝑡) − 𝑃(𝑡 − 1) ش١د

، tش١د ،ِٓضٌا ًضّ٠

ٟ٘ ،ٌٟبٌّا ًطلأا شوع ًضّ٠ P -

خللاوٌا 𝐸 𝑢_𝑡² - ٟف

داذ٘بشٌّا ِٓ ش١جو دذه شفٛز٠ بِذٕه خطبخ شفظٌا ٞٚبغ٠ ش١غزٌا ؾعٛزِ ْٛى٠ َّٛوٌا ٍٝهٚ ،شفظٌا ٞٚبغ٠ ؾعٛزٌّا ْٛى٠ بِذٕه هٌرٚ ،ٓ٠بجزٌا خم١مذٌا شفظٌا يٛد شكبٕزِ داش١غزٌا ن٠صٛر خجظ٠ ٟو١جـٌا ْٛٔبمٌٍ حش٘بلٌا مبؼخئثٚ

.

(43)

𝑌 𝜏 = 𝑙𝑜𝑔

_𝑒

⁡[𝑃 𝑡 + 𝜏 𝑃 𝑡 ] σ

_𝑌(τ)

σ

_𝑌(τ)

𝜎

_{𝑌 𝜏}

= 𝐸 𝑌

²

− [𝐸 𝑌 ]

²

(22.1)

𝐸 𝑌 𝑃

𝜏

: عىًجي مثًٌ

و مك ءاهتنا دنع يزاٍعي فاسحنا k ج

ًنيش لا 𝛿

ىٍسقت دنع كنذو ،

ًهكنا ًنيصنا لاجًنا 𝜏

ىنإ سٍغص ًنيش لاجي k 𝛿

ةباتك نكًٌ هٍهعو ، 𝑘 = 𝜏 𝛿

.

𝜎

^′

: سٍغصنا ًنيصنا لاجًنا ىهع سعسنا ًف سٍغتهن يزاٍعًنا فاسحنلاا مثًٌ

𝛿 اره سبتعا اي اذإ و ،

ًنيصنا لاجًنا لىط ىهع ٍواستي يزاٍعًنا فاسحنلاا 𝜏

ني يأ 𝛿

ىنإ 𝑘𝛿 ةغٍصنا ةباتك نكًٌ ،

𝑌 𝜏

= 𝜏 𝛿 𝜎′

FAMA 1965

_𝑡−1

𝑥

_𝑡−2

Correlation Coefficient Test 𝑟

_𝜏

1 (𝑝

_𝑡

− 𝑝

_𝑡−1

)

= 𝐸 𝑢

_𝑡²

− 𝐸 𝑢

_𝑡

² 𝑡

1 +1 ≥ 𝑟

_𝜏

≥ −1 1

𝑟

_𝜏

1

𝜏

حبثسلأٌ ن٠صٛر سٚذد ذٕه 1

ساذمّث 𝑑 خلذٌٍا ٟف ش١غزٌا تغذ٠ t

𝑢_𝑡+1 خم٠شـٌبث 𝑢_𝑡+1 = 𝑙𝑜𝑔_𝑒⁡(𝑝_𝑡+1+ 𝑑) − 𝑙𝑜𝑔_𝑒(𝑝_𝑡) :

.

خللاوٌبث تزى٠ ْأ ؽبجرسلاا ًِبوِ ٟف ًطلأا ْأ قدلا 2

𝑟_𝜏 = ^𝑐𝑜𝑣 ^𝑡^,𝑢^𝑡−1 :

𝑉 𝑢_𝑡 𝑉 𝑢_𝑡−1 ْبو بٌّ ٓىٌ

𝑉 𝑢_𝑡 ≈ 𝑉 𝑢_𝑡−1

ُر ٗٔئف غ٠ٛور 𝑉 𝑢_𝑡−1 ـث

𝑉 𝑢_𝑡 خللاوٌا ٍٝه ًظذٔ ب٘ذٕه (1.7)

.

(45)

0

𝜏

01 01 1

10 FAMA, Eugene :The Behavior of the stock-Market Prices, Journal of Business, ,The university of Chicago Press, V 38, I(1), Jan.1965, P73.

: 1999،504

(46)

2 Test of Runs

Roberts Run

0 03

0 1 2

3 Filter Technique

5 % 5

%

5 % Alexander 1961

2

1 Roberts : op. c it, P09.

ٟم١جـزٌا ًظفٌا ٟف ً١ظفر شضوأ ًىشث داسبجزخلاا ٖز٘ ٌٝإ قشـزٌبث َٛمٕع رإ ،خ١ٍّوٌا ً١طبفر ٟف يٛخذٌا ْٚد ؾمف داسبجزخلاٌ فطٚ ءبـهئث ٟفزىٕع 2

.

فبفزدلاا ٚ ءاشزشلاا خعب١ع ٓه خفٍزخٌّا ٜشخلأا حبثسلأا ٟ٘ خ٠دبوٌا ش١غ حبثسلأا 3

Buy-and-Ho ld .

4Eugene F. FAMA: Efficient Capita l Markets: A Rev iew of Theory and Empirical Work, Journal of Finance, 25(2), 1970, P3 95.

(47)

Mandelbrot Bachelier

𝑃 𝑡 + 𝑇 − 𝑃 𝑡 T

0 𝑇 T

T Mandelbrot

Stable Paritian Distribution 𝑡, 𝑇 =

𝑙𝑜𝑔

_𝑒

𝑃 𝑡 + 𝑇 − 𝑙𝑜𝑔

_𝑒

𝑃 𝑡 𝐿 𝑡, 𝑇

𝑇

01 σ

²

σ

²

5 Levy

𝑓 𝑡 𝑙𝑜𝑔 𝑓 𝑡 = 𝑙𝑜𝑔𝐸 𝑒

^𝑖𝑢𝑡

= 𝑖𝛿𝑡 − 𝛾 𝑡

^𝛼

1 + 𝑖𝛽 𝑡/ 𝑡 𝑤 𝑡, 𝛼 (27.1)

𝑡 u −1 𝑖

𝑤 𝑡,𝛼 = 𝑡𝑎𝑛 𝜋𝛼

2 , 𝛼 ≠ 1, 𝜋

2 𝑙𝑜𝑔 𝑡 , 𝛼 = 1.

(27.1)

1 Eugene F. FAMA: ―The Behavior of the stock-Market Prices‖, Journal of Business, ,The university of Ch icago Press, V 38,Issue 1, Jan.1965, P101.

(48)

𝛼 Characteristic Exponent

0 < 𝛼 ≤ 2 𝛼

𝛼 = 2  0 < 𝛼 < 2  𝛼

2 0 1 < 𝛼 < 2

𝛼 = 2

β Index of Skewness

−1 < β < +1

β = 0  Symetric

0 < β < +1  β

1 −1 < β < 0  β

1 δ Location Parameter

γ Scale Parameter γ

Pr=0.25 Pr=0.75

𝑙𝑜𝑔 𝑓 𝑡 = 𝑖𝜇𝑡 − 𝜎

²

2 𝑡

²

(28.1) 𝛼 = 2

𝛽 = 0 𝛿 = 𝜇

𝛾 =

^𝜎²

2

FAMA 1965 12.1

1 Eugene F. FAMA: « Mandelbrot and the Stable Paretian Hypothesis », The Journal of Business , the university of Chicago Press, V36, Issue 4, Oct. 1963, P421-422.

(49)

12.1 يعيبطلا عيزىتلا راعسلأل يمتيراغىللا ريغتلا عيزىت

Eugene, op. cit, Jan.1965, P48.

FAMA

03 11

30 Changing Parameters Non -

Stationarity 𝜎

²

α

α 2

𝛼 < 2 2

1966 1965

خ١ٌبزٌا خـ١غجٌا خللاوٌبث بً١ػب٠س ساشمزعلاا فشو٠ 1

: خٌاذٌا ْأ يٛمٔ

ِٓضٌٍ خجغٌٕبث حشمزغِ 𝑥

خللاوٌا كمذر ذٔبو ارإ 𝑓_𝑥 𝑥, 𝑡 = 𝑓_𝑥 𝑥

ؾغثأ ٛ٘ٚ ،

ساشمزعلاٌ َٛٙفِ

Stationarity .

2 Eugene F.FAMA, et al.: « The Adjustment of Stock Prices to New Informat ion », International Economic Rev iew, 10(1), February 1969, 1–21.

(50)

Stock Split NYSE 1927

1959 940

_𝑡

𝑗

𝑡

_𝑗𝑡

Residual 29.1

30

𝑗𝑡

30 𝑢

_𝑚

=

^𝑁_{𝑗 =1}^𝑚

𝑢

_𝑗𝑚

𝑁

_𝑚

(30.1)

𝑢

_𝑗

𝑗

𝑚 𝑚

−29 ≤

𝑚 ≤ 30 𝑚

𝑚 = 0

𝑁

_𝑚

1 : an Effic ient Market « a market that adjusts rapidly to the new information »

سبظزخلابث خعاسذٌا ٖز٘ شٙزشر 2

ّٟ٘بغٌٍّ سبظزخا ٛ٘ٚ ،FFJR

ْ

ُ٘ٚ بٙ١ف FAMA – FISHER – JENSEN – ROLL :

.

:3

حؤشٌّٕا يبِ طأس ٞ خٍطبذٌا ٜشخلأا داسٛـزٌا ٟغٍ٠ ش١ذث ،شش١ف خم٠شـث خجشٌّا شوغٌا ٗٔأ ٟجغٌٕا شوغٌبث ٟٕؤ

.

(51)

𝑚

𝑢

_𝑗𝑡

29.1 𝑢

_𝑚

𝑢

_𝑘

(𝑘 = −29)

(𝑘 = 𝑚) 𝑈

_𝑚

𝑈

_𝑚

= 𝑢

_𝑘

𝑚

𝑘=−29

(31.1)

ٓ١١ٌبزٌا ٓ١ٍىشٌا ٟف خظخٍِ FFJR :

ًىشٌا ( ) 13.1 : خعاسذٌ بًمفٚ خئضجزٌا دب١ٍّه ن١ّجٌ خجغٌٕبث طرٌّٕٛا ٟلبث ؾعٛزِ

. FFJR

-

u

m- يقابلا طسىتم

-m- مهسلا تئسجت خيراتل تبسنلاب رهشلا

سذظٌّا :

FAMA, Eugene F. et al.: «The Adjustment of Stock Prices to New Information », International Economic Review, 10(1), February 1969, P13.

ًىشٌا ( ) 14.1 : خعاسذٌ بًمفٚ خئضجزٌا دب١ٍّه ن١ّجٌ خجغٌٕبث طرٌّٕٛا ٟلبث ؾعٛزِ ُواشر . FFJR

-Um- يقابلا طسىتم مكارت

-m- مهسلا تئسجت خيراتل تبسنلاب رهشلا

FAMA, Eugene F. et al.: «The Adjustment of Stock Prices to New Information»,

International Economic Review, 10(1), February 1969, P13.

(52)

𝑚

13.1 14.1

FFJR Lintner

Implicit Information

Adjustment of the

price 13.1

14.1

(53)

1970 FAMA



Potential Sources

1Eugene F.FAMA: « Effic ient Capital Markets: A Revie w of Theory and Emp irica l Work , Journal of Finance, 25(2), 1970, P387.

2 Eugene F.FAMA: «Random Walks in Stock Market Prices, Financia l Analysts Journal , Jan-Feb 1995, P76.

ٍٟطلأا ضٌٕا 3

:

» An efficient market is defined as a market where there are large nu mbers of rational, profit -maximizers actively competing, with each trying to predict future ma rket va lues of individual securities, and where important current informat ion is almost free ly available to a ll partic ipants« .

(54)

1 2 3

1 The Weak Form

Random Walk 1

2 𝑓 𝑟

_{𝑗 ,𝑡+1}

Φ

_𝑡

= 𝑓 𝑟

_{𝑗 ,𝑡+1}

(32.1) 𝑟

_𝑖,𝑡+1

𝑓 𝑡

Φ

_𝑡

𝑡 𝑟

_{𝑗 ,𝑡}

, 𝑟

_{𝑗 ,𝑡−1}

, 𝑟

_{𝑗 ,𝑡−2}

…

يٛمٔ ب٘ذٕه ذئبه نِ خ١ئاٛشوٌا خوشذٌا ذٔبو ارإ بِأ 1

:

» خمزشّث خ١ئاٛشه خوشد Random wa lk with drift »

ٓه فٍزخ٠ نلٛزٌّا ذئبوٌا ْبو ارإ هٌرٚ ،

شفظٌا .

(55)

Fama 1965

𝑡 + 1

𝑟

_{𝑚 ,𝑡+1}

𝑡 + 1

𝜎 𝑟

_{𝑚 ,𝑡+1}

Φ

_𝑡

Φ

_t

m

29.1 FFJR

_{𝑗 ,𝑡+1}

𝑗

𝑡 + 1

39.1

1 Eugene F. FAMA; James D. Mac Beth: «Risk, Return, and Equilibriu m: Emp irica l Tests», The Journal of Politica l Economy, Vo l. 81, No. 3. (May - Jun., 1973), pp. 607-636.

حشلٔ ٓه شجو٠ قٛغٌا طرّٛٔ ْأ ٛ٘ قشفٌا ،خ١ـخ خٌدبوِ ٓه حسبجه ٛ٘ ٞزٌا ًىشٌا خ١دبٔ ِٓ قٛغٌا طرّٛٔٚ ةسبش طرّٛٔ ٓ١ث ش١جو ٗثبشر نبٕ٘ خم١مد 2

ٌٟبٌّا ًطلأا شوع ٗىٍع ٞزٌا سبغٌّا ٓه شجو٠ قٛغٌا طرّٛٔ ٓىٌ ،شؿبخٌّاٚ ذئبوٌا ٗ٠ذوث ش١د ِٓ بًّئاد خمدلاٌا حشزفٌٍ سبّضزعلاا ًجمزغٌّ خ١ٌبذٌا شّضزغٌّا بّٙرار ٓ٠ذوجٌٍ خ١ـخ خٌدبوِ ًك ٟف -

شؿبخٌّاٚ ذئبوٌا –

خمثبغٌا حشزفٌٍ ٓىٌ

.

(57)

𝑗 1

m 𝛽

_𝑗

_𝑗𝑡

𝐸 𝜂

_𝑗

= 0

NYSE 1926

1968

Fair Game

2 The Semi-Strong Form

(58)

FFJR (29.1)

_𝑗𝑡

Residual 29.1

𝑢

_𝑗𝑡

30 𝑢

_𝑗𝑚

30 30.1

𝑗 𝑈

_𝑚

0 (31.1)

FFJR 1969

Scholes

Selling Pressure

FFJR

3 The Strong Form

Fama

1R. Cobbeau : « Théorie Financière », », 2^e édition, Econo mica, Pa ris, 2003,P319.

(59)

Osborne &

Niederhoffer NYSE

Scholes

Professionals

Jensen 1967

Jensen

115 1945

1964

𝑟

_𝑗,𝑡

− 𝑟

_𝑓,𝑡

= 𝛼

_𝑗

+ 𝛽

_𝑗

+ 𝜀

_{𝑗 ,𝑡}

𝑟

_𝑀,𝑡

− 𝑟

_𝑓,𝑡

+ 𝑢

_{𝑗 ,𝑡}

(40.1)

𝛼

𝑢

_{𝑗 ,𝑡}

𝐸 𝑢

_,𝑡

= 0

(40.1)

1Eugene F. FAMA: Efficient Capita l Markets: A Rev iew of Theory and Empirical Work, Journal of Finance, 25(2), 1970, P409-410.

(60)

10

= 0

𝐸 𝑢

_{𝑗 ,𝑡}

= 0

(41.1) CAPM

Φ

_𝑡

j β

_j

Φ

_𝑡

15.1 m

15.1 FAMA, Eugene F.: Efficient Capital Markets: «A Review of Theory and Empirical

Work», Journal of Finance, 25(2), 1970, P411.

(61)

Jensen

CRSP

²

1962 Autocorrelation

Lo & MacKinlay

1988 NYSE

Diversification 1986

French & Roll

Non-Stationarity

13 Black

Noise Debont & Thaler 1987

NYSE 3

5

1 Michael C JENSEN: « Some Anoma lies evidence regarding ma rket e fficiency » , Journal of Financial Economics, 6(2–3), 1978, P95.

2 Center for Research in Security Prices.

3 Eugene F. FAMA: Effic ient Capital Ma rkets:II » , Journal of Finance, 46(5), 1991, P1575-1577.

(62)

Sharp CAPM

Fama 1965 1

2

(63)

59 probability Space 𝛺, ℱ, ℱ

_𝑡 _𝑡

, 𝑃

ω ω ∈ Ω

Ω

ω ℱ

A

𝐴 ⊂ 𝛺 ℱ

Ω ℱ

_t

ℱ

_𝑡

⊆ ℱ

_𝑢

⊆ ℱ t

𝑡 ≤ 𝑢 ℱ

ℱ

_{𝑡 ≥0}

Filtration

(64)

60 Stochastic Process

Infinite Information

Structure Filtration

𝑇

₀

𝑇

₁

02 02 02

𝑇

₁

08 16 Patition

𝑇

₁

Filtration

.

(65)

61 Filtration σ t

Random Process

Discrete Stochastic Process Continuous Stochastic Process

Markov series

Weiner Process

تظضٌٍا ًف تٕىٌّّا ثاذصلأا ْأ يأ 1

ـب اًفٍس اٍٍٙػ شبؼٌّاٚ تٕىٌّّا ثاذصلأٌ تٍٍىٌا تػّٛزٌّا ٓػ دشخت لا t

ℱ .

2 GOFFIN R. : « Principes de la Finance Moderne », 3^e édition, Econo mica , Pa ris, 2001, P371.

(66)

62 Weiner Process Brownian Motion

𝑧

𝛿𝑧  𝛿𝑡

𝛿𝑧 = 𝜀 𝛿𝑡 (1.2)

𝜀 𝜙 0,1

𝛿𝑧  𝛿𝑡

𝑊

_{𝑡 ≥0}

𝑊

₀

= 0 1 t=0

𝑡 → 𝑊

_t

2 ∀𝑡 ∈ 𝑅

⁺

3 ∀𝑠 ∈ 0,𝑡 (𝑊

_𝑡

− 𝑊

_𝑠

)

𝜙 𝜇

_𝑡−𝑠

, 𝜎 𝑡 − 𝑠 𝑧

T

𝑧 𝑇 − 𝑧(0) T

N

𝛿𝑡 𝑁 =

^𝑇

𝛿𝑡

𝑧 𝑇 − 𝑧 0 = 𝜀

_𝑖

𝛿𝑡

𝑁

𝑖=1

2.2 𝜀

_𝑖

(𝑖 = 1,2,… , 𝑁) 𝜙 0,1

𝜀

_𝑖

2.2 𝑧 𝑇 − 𝑧(0)

μ = 0 𝑁𝛿𝑡 = 𝑇

𝑇 Standard Weiner Process

𝑑𝑥

𝑑𝑥 = 𝑎𝑑𝑡 + 𝑏𝑑𝑧 (3.2)

تللاؼٌا ْأب ظصلا 1

( )1.2 تللاؼٌا ً٘ٚ ٗتساسد ًف ٌٍٍٗٛشاب اٙغاص ًتٌا اٙسفٔ ً٘

(21.1)

(67)

63 𝑎𝑑𝑡 𝑏𝑑𝑧

𝑎 𝑏

𝒂𝒅𝒕 1 𝑑𝑥

𝑑𝑡

(3.2)

𝑑𝑥 = 𝑎𝑑𝑡 𝑑𝑥 𝑑𝑡 = 𝑎

𝑎 𝑥

01 𝑎 𝑥

𝑥 = 𝑥

₀

+ 𝑎𝑡 (4.2)

𝑥

₀

0 T

𝑥 aT

𝒃𝒅𝒛 2 𝑏

Noise 𝑑𝑧

𝑑𝑡 Stationarity

𝑑𝑧 𝑏

𝑑𝑧 1,0

𝛿𝑥 𝛿𝑡 x

(1.2) (3.2)

δ 𝑥 = 𝑎𝛿𝑡 + 𝑏𝜀 𝛿𝑡 (5.2) 𝜀

δ 𝑥

𝜇 = 𝑎𝛿𝑡

𝜎 = 𝑏 𝛿𝑡

(68)

64 𝑉 = 𝑏²𝛿𝑡 5.2

Weiner

Process with Drift (1.2)

a=0.3, b=0.5

J. Hull : « Options, Futures et Autres Actifs Dérivées », Pearson Education, France, 2004, P….

𝑎 𝑏

Itô Process 𝑎 𝑏 Itô Process

𝑎 𝑏 𝑥

𝑡

𝑑𝑥 = 𝑎 𝑥, 𝑡 𝑑𝑡 + 𝑏 𝑥, 𝑡 𝑑𝑧 (6.2) t

t+1 x

𝑥 + 𝛿𝑥 𝛿𝑥 = 𝑎 𝑥, 𝑡 𝛿𝑡 + 𝑏 𝑥, 𝑡 𝜀 𝛿𝑡

ٛتٌإ يصٍٛو ّٗسا ًٔاباٌ ًضاٌس ٛ٘ٚ كسٌٕا از٘ غئاصٌ تٍّستٌا ٖز٘ دٛؼت 1

Kiyosi Itô

ًضاٌّا ْشمٌا ِٓ ثإٍسّخٌا ٚ ثإٍؼبسلأا ًف هٌر ْاوٚ ، .

𝑑𝑥 = 𝑎𝑑𝑡 + 𝑏𝑑𝑧

َاؼٌا شٌٕاٚ كسٔ

𝑑𝑥 = 𝑎𝑑𝑡

𝑑𝑧

شٌٕاٚ كسٔ

𝑥

شٍغتٌّا تٍّل

ِٓضٌا

(69)

65 (6.2)

𝑎 𝑥, 𝑡 𝑏² 𝑥, 𝑡

Itô lemma Itô lemma Stochastic Deffirential Equations 6.2

𝑑𝑧

G t

x 𝑑𝐺 = 𝜕𝐺

𝜕𝑥 𝑎 𝑥, 𝑡 + 𝜕𝐺

𝜕𝑡 + 1 2

𝜕

²

𝐺

𝜕𝑥² 𝑏

²

𝑥, 𝑡 𝑑𝑡 + 𝜕𝐺

𝜕𝑥 𝑏 𝑥, 𝑡 𝑑𝑧 (7.2)

𝜕𝐺

𝑏

²

𝑥, 𝑡 𝑑𝑧

𝑎 𝑥, 𝑡

𝑏 𝑥, 𝑡

(70)

66 𝛿𝑥 x ]-∞,+∞[

𝑥 ∈ 0,+∞

𝛿𝑥 ∈ −𝑥,+∞

Log-Normal

25.1 1965

 Yield

𝑥

_𝑡

𝑡

𝑥

_𝑡+1

^𝑙𝑜𝑔^𝑒^(𝑥^𝑡+1^{)−𝑙𝑜𝑔}^𝑒^(𝑥^𝑡⁾

(8.2)

 Moore

%15 ± 

Osborne 1959 NYSE

2.2 3 2

1 FAMA, Eugene ,The Behavior of the stock-Market Prices, Journal of Business, ,The university of Chicago Press, V 38, I(1), Jan.1965, P45-46.

تللاؼٌا 2 (24.2) ةشىفٌا ٖز٘ شضٛت ًصفٌا از٘ ِٓ

.

(71)

67 2.2 31

1956 NYSE

OSBORNE M.F.: Brownian Motion in the Stock Market, Operations Research, 7(2), 1959, P147.

3.2 4.2 5.2

𝑙𝑜𝑔

_𝑒

𝑃 4.2 31

1956

NYSE OSBORNE M.F : op. cit, 1959, P149.

0,00 0,10 0,20 0,30 0,40 0,50

0 1 2 3 4 5 6 7

(72)

68

5.2 MATHIS J. : « Gestion d’actifs », Economica, Paris, 2002, P44.

GMB Geometric Brownian Motion

GMB

3.2 GMB 𝑑𝑥 = 𝛼𝑥𝑑𝑡 + 𝜎𝑥𝑑𝑧 (9.2)

𝛼 𝜎 (9.2)

(6.2) 𝑎 𝑥, 𝑡 = 𝛼𝑥

𝑏 𝑥, 𝑡 = 𝜎𝑥

1 GMB

GMB

log-normal GMB

(7.2)

0 0,1 0,2 0,3 0,4 0,5

-6 -4 -2 0 2 4 6

(73)

69 (9.2) 𝐺 = 𝑙𝑜𝑔

_𝑒

𝑥

𝝏𝑮

𝝏𝒕

= 𝟎 𝐺

𝝏𝑮

𝝏𝒙

=

^𝟏

𝐺

𝐱

𝝏^𝟐𝑮

𝝏𝒙^𝟐

= −

^𝟏

𝒙^𝟐

𝐺

(7.2) 𝑥, 𝑡 = 𝑎𝑥

𝑏 𝑥, 𝑡 = 𝜎𝑥

₀

∼ 𝒩 𝛼 − 𝜎

²

2 𝑇, 𝜎 𝑇 (11.2) T

𝛼 −

^𝜎₂²

𝑇 𝜎 𝑇

𝑙𝑜𝑔

_𝑒

𝑥

_𝑇

∼ 𝒩 𝑙𝑜𝑔

_𝑒

𝑥

₀

+ 𝛼 − 𝜎

²

2 𝑇, 𝜎 𝑇 (12.2) T

𝑙𝑜𝑔

_𝑒

𝑥

₀

+ 𝛼 −

^𝜎²

2

𝑇

𝜎 𝑇

(74)

70 3.2 𝐸 𝑥

_𝑡

= 𝑥

₀

𝑒

^𝜇𝑇

σ

²

𝑥

_𝑇

= 𝑥

²

𝑒

^2𝜇𝑇

(𝑒

^𝜎²^𝑇

− 1)

3 T 0

S 𝑆

_𝑇

T

𝑆

_𝑇

= 𝑆𝑒

^𝜂𝑇

𝑒

^𝜂𝑇

= 𝑆

_𝑇

𝑆 𝜂 = 1

𝑇 (𝑙𝑜𝑔

_𝑒

𝑆

_𝑇

− 𝑙𝑜𝑔

_𝑒

𝑆)

(11.2) 𝜂 ∼ 𝒩 𝛼 − 𝜎

²

2 , 𝜎 1

𝑇 (13.2) T

𝛼 −

^𝜎₂²

𝜎

T

𝑇

Fair game

1900

1959

(75)

71 Binomial Model

N 𝑆

𝑢𝑆

𝑑𝑆 6.2

10 𝑢 = 1,10 %

5 𝑑 = 1,10 %

Volatility

𝑝 𝑞 𝑝

Δ𝑡 .

سذصٌّا :

GOFFIN R. : « Principes de la Finance Moderne », 3

^e

édition, Economica, Paris, 2001, P418.

1Marek Capinski & Tomasz Zastawniak :" Mathematics for Finance – An Introduction to Financial Engineering" , Springer, London, 2003, P56.