الهندسة المالية



ةيعماجلا ةنسلا

:

2018

/

2019

)))((((

تايوتحلما سرهف

I I أ 01 01 04 10 12 12 15 19 28 30 30 34 39 40 40 47 57 65 68 68 75 83 97 99 99 99 103 107

تايوتحلما سرهف

مــــــــــيدقت

1 I .   

2 Freeman  Robin Finshman II . 

4 McCaw

Celluar, Cabevision, Barnes & Noble…

Financial Engineering

I .

5 Financial Engineering    Don M Chance Smith

6

II .

7

.

Fisher Black & Rechard Roll

The

International Association of Financial Engineering (IAFE)

8 . . efficiency effectiveness 

9



10 . . . 2007 . islamfin.go-forum.net/t2175-topic; le : 28/12/2018, à 22:39 . alnoor.se/article.asp?id=45134; le: 21/12/2018, à 00:21

6. David H. Gowland , Financial Innovation in Theory and

Practice, Surveys in Monetary Economics : (volume 2 : 1991, Oxford).

7. Don M. Chance , Robert Brooks, An lntroduction to Derivatives and Risk Management, (Thomson Higher Education by South-Western, Seventh Edition, Canada, 2006).

8. Franklin Allen, Glenn Yago, Financing the Future : Market-Based Innovations for growth, (series on Financial Innovation : 2010, Wharton school Publishing, Milken Institute, new Jersey).

9. Frederic Mishkin, The Economics of Money, Banking, and Financial Markets , (Addison Wesley, Boston, 7th edition, 2007).

10. Jean Marck Moulin, le droit de l’ingénierie financière, Gualino l’extenso éditions, 4° édition

11. Georges Legros, Ingénierie financière, fusions acquisitions et autres restructurations des fonds capitaux, Dunod

11

12. Peter Tufano, Financial Innovation, (June 16, 2002, Harvard Business School)

13. Yuh-Dauh Lyuu, Financial Engineering and Computation : Principles, Mathematics, Algorithms, (United Kingdom Cambridge University Press,USA, 2004).

14. Çigdem Izgi kogar, Financial Innovations and Monetary Control ,The Central Bank of the republic of Turkey, May 1995 ; sur le site :

12 I . 1 . 2 . أ . ب .

13 ج . د . ه . و . ز . 3 . أ .

14 ب . ج . II . I .  

15       

16

–







Taux de rendement réel

Taux d’inflation

RT

17

.

.

18

.

.

19 . P/E -. X

20

I .

21 𝑉 𝐶𝐹𝑡 II . g 10 5

22 D0 g 1 g D1 = D0 (g+1) D2 = D1 (g+1) D3 = D2 (g+1) = D1 (g+1) 2 D1 D2 D3 ... 𝑃₀ = 𝐷1 1 + 𝑟 + 𝐷₁(1 + 𝑔) (1 + 𝑟)2 + 𝐷₁(1 + 𝑔)2 (1 + 𝑟)3 + ⋯ ∞ 1 . Zero-Growth Model

23



    1 0 ) 1 ( k t t r D P t D D D D     _{3 2 1}      1 1 0 ) 1 ( 1 t r t D P r D P 1 0  0 P 1 D t ke 𝑃₀ = 5 0.05 = 100 2 . Constant-Growth Model 𝑃₀ = 𝐷𝑖 (𝑟 − 𝑔)

24 P0 Di r g 5 6 % 20 𝑃₀ = 5 (1 + 0,06) (0,2 − 0,06) = 37,86 37.86 37.86 3 . Variable-Growth Model) . : 𝑃₀ = 𝐷0 1 + 𝑔1 𝑡 (1 + 𝑟)𝑡 𝑛 𝑡=1 + 𝐷𝑛 1 + 𝑔2 𝑡−𝑛 (1 + 𝑟)𝑡 𝑡−𝑛 g1 g2

25 P0 D0 Dn r III . BATES BPA P PER BPA Price Earming 1 g n

1

,

0

1

1

1

1

1

,

0

1

1

0

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

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

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

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

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

n n n

g

r

r

g

g

q

g

r

PER

PER

IV .

26 1 . ) ( ) 1 ( ) 1 ( ) 1 ( 1 1 1 2 2 1 1 1 1 1 1 0 g r r g g D g r r g D P _T T T                                1 g 1 2 g 2 : T 2 . MOLODOVSKY 2 1 1 1 1 1 1 1 1 1 1 1 0 1 ) 1 ( ) ( ) 1 ( ) 1 ( ) ( ) 1 ( ) 1 ( 1 1 1 g r r j g g D r j g r g D r g g r D P N T N j T N t t t j T T T                                  







27 1 g 2 g ) ( j g T N

28 1 . 2 . 3 . 4 . 5 . ) 2006 ( 6 . 7 . 8 . 2016 9 . 2010 10 . 2006 11 . 12 . 2010

29

13. Abdelkader beltas, , Marché des capitaux et la structure par échéance des

taux d’intérêt, )Edition LEGENDE, 2008, Alger(.

14. Valuation of Bonds and Stock

https://www.scranton.edu/faculty/hussain/teaching/mba503c/MBA503C03.pdf

15. Valuation of Financial Instruments: TheoreticalOverviewwith Applications in Bloomberg,

30 .   2 . أ . ب . ج .

31 د . ه . و . ز . ح . ط . ي . 3 . أ . 

32  ب .   ج .    د .   coupon

33  ه .   LIBOR و .   ز .

34 I . . n n n r F r C r C r C r C P ) 1 ( ) 1 ( ) 1 ( ) 1 ( 1 3 3 2 2 1 0             n C C C₁  ₂ 











n



n n n r F r r r C P r F r r r C P                          ) 1 ( ) 1 ( ) 1 ( 1 ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( 1 1 1 0 2 1 0   -1 1+r 1 n n n r F r r r C P     _{ }             (1 ) ) 1 ( 1 ) 1 ( 1 ) 1 ( 1 ₁ 0 n n r F r r C P        1 (1 ) (1 ) 0 r r FA r V n r n n r n        ) 1 ( 1 ) 1 ( % , % , F V CFA P₀  _n,r%  _nr%

35 P0 C r n F I . 𝑃₀ = 𝐶₁(1 + 𝑟)−1 ∞ 𝑖−1 P0 Ct r C 𝑃₀ = 𝐶 (1 + 𝑟)−1 ∞ 𝑡=1

36 r C P r C r F r r C P n n n n n                 0 (1 ) lim 0 ) 1 ( 1 lim lim 𝑃₀ = 𝐶 𝑟 III . m i i i i m 1 1           m m r r r r m

37 mn mn mn n m m m m m m nxm m m n m m m r F m r m r m r m r C P m r F m r m r m r C P r F r r r C P                                                                                                                              1 1 1 1 1 1 ' 1 1 1 1 ' ) 1 ( ) 1 ( ) 1 ( ) 1 ( ' 1 2 1 1 0 2 1 0 2 1 0    1 1         m r 1 m.n n m n m m r F m r m r C P . . 0 1 1 1 '                    m C C % % 1 1 1 , , 0 . . 0 m r mn m r mn n m n m FV FA m C P m r F m r m r m C P                       III . m  

38 1 1 1 1 lim lim 1 1                              r r m m m m e r e m r r m r r







r r nr



nr r nr nr r r r n r n r r r r n n Fe e e e Ce P Fe e e e e C P e F e C e C e C e C P r F r C r C r C r C P                                                                      2 0 3 2 0 3 2 1 0 3 2 1 0 1 ) 1 1 ( ) 1 1 ( ) 1 1 ( ) 1 1 ( ) 1 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( r e 1 n nr r nr Fe e e C P             1 1 0

39 . . . . . . ) 2006 ( . . . .

40

I .

41  .  . K St Vt K -St St – K

42 10000 10200 200 II . 1 . حبر ةراسخ Vt St K 0 حبر ةراسخ Vt St K 0

43

First National Bank Rock Solid Insurance Company

2 .

44 III . . . . .   . IV .

45

V .

. .

46 . . - . -. - . . . . OTC - . - . -. - . - . .

47 - . I . 15 % 1 . 2 .

48 3 . 4 . 5 . II . 1 . BNP Paribas 9 2011 10 10 x 100 = 1000 56,822 56822 BNP Paribas 10 x 100 = 1000 56,471 56471 2 .

49 900000 $ 950000 $ 50000 $ 500000 $ 420000 $ 410000 $ 413000 $ 398000 $ 7000 $ ( 420000 – 413000 ) ، 12000 $ ( 410000 -398000 ) 5000 $ ( 12000 -7000 ) 3 . DJIA

50 CAC40

4 .

51

LMM CME

16

52 0 008728 0 008758 0 008752 141491 141491 300 141094 IV . 1 . 2 .

53 3 . 1925 4 . 1 . Futures Commission Merchant

54 2 .  (  )

55 V . . Contract size . Delivery Terms Burns Harbor Saint Louis

56 3 . Limit up Limit down 4 . 1000 VI . 1 . 5 % و 15 %

57 2012 10000 2012 100 100 10 % 100000 2 . 98 100 98 x 10000 20000 80000 . 75 80 80 80000 75 = 100000 x 75 % = 75000

58 80000 96 ( = 98 – 96 ) x 10000 = 20000 = 80000 – 20000 = 60000 40000 4 . 03 10000 ( 96 x 10000 = ) 960000 1000000 = 1000000 – 960000 = 40000 60000 – 40000 = 20000 20000 VII .

59 06 20 06 20 I .

60 Vt = Ft-1 - Ft Vt Ft-1 Ft II .     T S0 F0 : 0 r : F0 = S0erT

F

0

> S

0

e

rT

F

0 P

61 F0 - S0e rT = P

F

0

< S

0

e

rT

F

0 P S0e rT - F0 = P F= SerT F=1150 e0.11 1/12 = 1160 . F= (S – I)erT نأ ملعلا عم I

62 . q F= Se(r-q)T F= 25 x e(0.1-0.0396)1 = 26,556 . أ . CAC40 10 %  RENAULT €  CAC40 €  RENAULT %

63  RENAULT €  € CAC40 F= 400000 x e(0,1)60/365– (200x20 e(0,1)45/365) = 402580 ب . q F F= Se(r-q)T CAC40 F= 4000e(0,06-0,01)x0,25 = 4050,3 . GBP S USD S GBP USD F F$ 1 £ (F$) . (1£) USD ـب r GBP وه rf

64 F= Se(r- rf)T F r rf r- rf ( rf ) ( r ) USD/EUR 1,1 F= 1.1e(0.03- 0.05)2 = 1.057

65 . . . . 2001 . . . . . . . .

66 13 . . . . . . . islamiccenter.kau.edu.sa/arabic/Hewar_Arbeaa/abs/219 ; le: 23/11/2012, à 23:55

20. Don M. Chance, Don M. Chance , Robert Brooks, An lntroduction to

Derivatives and Risk Management, (Thomson Higher Education by South-Western, Seventh Edition, Canada, 2006)

21. Frederic Mishkin, The Economics of Money, Banking, and Financial

Markets , (Addison Wesley, 7th edition, Boston, 2007)

22. John Hull, Options, Futures, and Other Derivatives, 9em, Pearson.

23. Lishang Jiang , Mathematical Modeling and Methods of Option Pricing,

(World Scientific Publishing, Singaphore, 2005)

24. Purcell Wayne, Koontz Stephen, Agricultural futures and options Principles

and Strategies, (Prentice Hall, 2’ed, États-Unis, 1998), p 257.

25. Rangarajan Sundaram, Sanjiv Das, Derivatives Principles and Practice,

(McGraw-Hill Education, New York, 2010)

26. Gaurav Dhingra, An Understanding Of Financial Derivatives, (Magazine

The chartered accountant, march 2004)

27. Forward and Futures Prices, September 11, 2006, p02, sur le site : www.uic.edu/cuppa/pa/academics/ABFM_database/Lectures/Prices.pdf,le: 18/02/2019,

67

28. Derivatives Market (Dealers) Module, NSE’s Certification in Financial

Markets, National Stock Exchange Of India Limited, 2010, sur le site :

www.nseindia.com/content/ncfm/DMDM_rev.pdf; le: 08/06/2018, à 23:05.

29. Ensuring efficient, safe and sound derivatives markets, Commission Of

The European Communities, Brussels, 03/07/2009, sur le site :

eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=COM:2009:0332:.le:6/04/2018, 30. How Stock Futures Work, Dave Roos, sur le site:

money.howstuffworks.com/personal-finance/financial-planning/stock-future1, le: 23/12/2018, à 19: 48

31. Le contrat à terme sur actions, sur le site:

comparabourse.fr/fiches-pratiques/contrat-a-terme-sur-actions., le: 23/121/2018, à 19: 51 32. Trading In Futures An Introduction, Chicago Board of Trade (CBOT),p

1, sur le site : www.cbot.com; le: 19/04/2019, à 22:48

68 أ .   ب . 

69  ج .   أ . 100 30 60 $ 3 $ 64 1 1 63 0 0 61 2 2 60 3 3

70 59 3 3 64 $ 60 $ 64 $ 64 $ 60 $ 4 $ 4 $ 3 $ 1 $ 64 $ 64 63 1 $ 61 $ 3 $ 61 $ 63 61 2 $ 60 $ 3 $ 63 $ 63 $

71 60 $ 59 $ 60 $ 59 $ و 59 $ 60 $ 60 -3 -3 60

72 ب . 100 € 7 € € 90 3 3 93 0 0 94 1 1 100 7 7 120 7 7

73 1 . 90 € 10 7 3 3 € 90 7 100 3 € 3 € 90 € 3 € 2 . 93 € أ 7 7 0 93 7 100 0 93 € 3 . 120 € 0 7 7 € 7 € 7 €

74 100 7 100 7 € 120 € 4 . 94 € 6 7 1 € 1 € 1 € 94 7 100 1 € 94 € 93 94 1 € 5 . 1 100 € 100 € 0 7 7 € 100 7 100 7 € 100 € حابرلأا / رئاسخ _{ةدوذحم ريغ حابرلأا} ةدوذحم رئاسخ مهسلل يقىسلا رعسلا 93 100 -7

75

I

.

VS E حابرلأا / رئاسخ مهسلل يقىسلا رعسلا 93 100 7 دوذحم حبر ريغ ةراسخ ةدوذحم

76 VS < E VS > E VS = E 1 . أ . ب . . .

77 Vt = Max ( Vm- V0 ), 0 ……….(17-2) Vt Vm . أ .    V0 = Max ( Vs- E ), 0

78 V0 Vs E 100 3 100 105 5 2 18 V0 = Max (Vs- E), 0 V0 = Max (105- 100), 0 = 5 2 100 200 6.5 $ 1.5 $ Vt = Max ( Vm- V0 ), 0 Vt = Max ( 6.5 - 5 ), 0 = 1.5 97 97

79 ب . V0 = Max (E - Vs ), 0    48 $ 44 $ 100 50 $ 2 $ 6 $ V0 = Max (E - Vs ), 0 V0 = Max (50 - 44 ), 0 = 6 6 $ 600 $ 200 $ 400 $

80 6.4 $ Vt = Max ( Vm- V0 ), 0 Vt = Max ( 6.4 - 6 ), 0 = 0.4 53 V0 = Max (50 - 53 ), 0 = 0 V . 1 .

81 2 . 3 . 4 . 5 .

82

6 .

7 .

83 Black-Scholes

I . The Binomial Model

William F.Sharpe 1978

Investments Cox, Ross & Rubinstein

1979

84 1 . 2 . أ . ب . ج . د .

85 3 . أ . C>=0 S E u d q 1-q Su Su = S (1 + u ) Sd Sd = S ( 1 + d ) d

86 C(u,d) = Max S(u,d) – E, 0

يأ : Cu = Max S(1+u) – E, 0 Cd = Max S(1+d) – E, 0 Cu Cd

Ca

Cu=} Max ]S(1+u) – E, 0[ { مهسلا رعس عفترا ارإ ءارشلا رايخ ةميق Cd =} Max ]S(1+d) – E, 0[ { مهسلا رعس ضفخنا ارإ ءارشلا رايخ ةميق

q

1-q

s

Su=S(1+u)

q

Sd=S(1+d)

(1-q)

q

(1-q)

87 Ca= qCu+(1-q)Cd / (1+rf) ب .



Su2=S (1+u) 2 Sud=S (1+u)(1+d) …………



Sd2=S (1+d) 2

88 Sdu=S (1+d)(1+u)



Cu2 = Max S(1+u)2 – E, 0

Cud= Max S(1+u)(1+d) – E, 0

89

 Cu= [qCu2 +(1 - q) CUd]/ (1+ r )

Cd= [qCud +(1 - q) Cd2]/ (1+ r) (q) =(1+ r – d ) / ( u – d ) C= [q Cu +(1 - q) Cd]/ (1+ r ) Cu Cd C= [q2 Cu2 +2q (1 - q) Cud+ (1 – q)2Cd2 ] / (1+ r )2 أ .

90 224

C

Cu

Cd

Cu

2

Cud

Cd

2

Cu

3

Cu

2

d

Cud

2

Cd

3

………

………

………

………

………

n=0 n=1 n=2 n=3 n

S

Su

Sd

Su

2

Sud

Sd

2

Su

3

Su

2

d

Sud

2

Sd

3

………

………

………

………

………

n=0 n=1 n=2 n=3 n

91 𝑪𝒂 = 𝟏 (𝟏 + 𝒓)𝒏 𝒏! 𝒏 − 𝒌 ! 𝒌! 𝒒 𝒌_{(𝟏 − 𝒒)}𝒏−𝒌 _{𝑴𝒂𝒙 𝑪𝒖}𝒌_𝒅𝒏−𝒌_{− 𝑬 , 𝟎} 𝒏 𝒌=𝟎 Ca k n q q= (1+r-d)/(u-d) 1+q u d II . The Black-Scholes Model

92 ج . . . أ . ب .

93 ج . د . ه . و . . Ca = P[N(d1)] – E e-r t[N(d2)] d1 = [ln (P/E) + (r +  2 /2) t] / t d2 = d1 - t Ca P N(di) N(d1) ، N(d2) E e r ln (P/E) : P/E 2  Ca P E t

94 365 r N(d1) ، N(d2) 2

P = 20$ E = 20$ t = 3 mois (0,25 ans) r = 0,064 = 6,4% 2 = 0,16  = 40% d1 d2 d1 = [ln (20/20) + (0,064 + 0,16/2) 0,25] / 0,400,25 = 0,18 d2 = 0,18- 0,400,25 = - 0,02 N(d1) = N(0,18) N(d2) = N(-0,02) d1 = 0,18 0,5714 d2 = -0,02 0,4920 ( 2 -25 :) Ca = 20[N(0,18)] – 20 e- (0,064)(0,25)[N(-0,02)] = 1,74$ P E t r 2 Ca

95 20$ 20$ 0,25 6,4% 0,16 1,74$ 25 20 0,25 6,4 0,16 5,57 20 25 0,25 6,4 0,16 0,34 20 20 0,50 6,4 0,16 2,54 20 20 0,25 9 0,16 1,81 2 20 20 0,25 6,4 0,25 2,13 أ . $ $ $ $ $ ) 5 $ ب . $ ج . $ . د . $

96 E e-r t N(d1) N(d2) ه . $ . Pu = Ca + Pv (E) - P Pu : Ca : Pv (E) : P : Ca Pu e-r t[1- N(d2)] – P [1 - N(d1)] Pu e- 0,064(0,25)[1- 0,4920] – 20 [1 – 0,5714] Pu

97 . . . . . 6 . . . . . . .

98

. .

. ac.ly/vb/showthread.php?p=2316 ; le : 27-03-2019, à 14 :43

Don M. Chance , Robert Brooks, An lntroduction to Derivatives and Risk Management, (Thomson Higher Education by South-Western, Seventh Edition, Canada, 2006).

17. Mondher bellah, yves simon, Options, contrats à térme et gestion des risque,

(Economica edition, France, 2000)

18. Rainer Brosch, Portfolios of Real option, (Springer edition, Berlin, 2008) 19. Rangarajan Sundaram, Sanjiv Das, Derivatives Principles and Practice,

(McGraw-Hill Education, 2010).

20. Finance 100 Problem Set Options (Alternative Solutions), sur le site : finance.wharton.upenn.edu.pdf ; le : 20/ 02 / 2019, à 20 :59

99 . 5 5 I .

100 . LIBOR 3 12 3 2010 7 % 2012 7 % LIBOR 6 LIBOR 6 % LIBOR 1 6 % 6 7 1 % 10000 7 6 1 % 10000

101 2 3 4 8 % 7 % 9 % 8 7 1 % 10000 7 7 0 9 7 2 % 20000 7 8 1 % 10000 7 7 0 7 9 2 % 20000 II . BFt Bvt

𝐵

_𝐹𝑡

=

𝐶 (1+ 𝑅_{0 𝑡})𝑡 𝑛 𝑡=1

+

𝐹 (1+ 𝑅_{0 𝑛})𝑛

𝐵

_𝑣𝑡

=

𝐶 (1+ 𝑅_{0 𝑡})𝑡 𝑛 𝑡=1

+

𝐹 (1+ 𝑅_{0 𝑛})𝑛 F

102 C : C : t 0Rt : . St BFt Bvt ، St = BFt - Bvt LIBOR 8 % 100 3 9 15 10 % 10,5 % 11 % LIBOR 10,2 % C = 4 C = 5.1 𝐵_𝐹𝑡 = 4 (1 + 0,10)123 + 4 (1 + 0,105)129 + 104 (1 + 0,11)1512 BFt = 98.79 millions 𝐵_𝑣𝑡 = 5.1 (1 + 0,102)123 + 5.1 (1 + 0,102)129 + 105,1 (1 + 0,102)1512 Bvt = 102.806 millions St 4,016 St = BFt - Bvt = 98,79 – 102,806 = -4,016 millions

103 I . 2 3 6 2 2 2.10 . . . . rate Swap 2.10 2 0.10 . 70 78 8.5% 5% 10% 6% x 100 x 360 70 x 8,5 6 100 x 180 360 1,75 x 0,5 0,875 70 0,875 70,875 78 x 10 5 100 x 180 360 1,75 x 0,5 1,95

104 7 8 1,95 71,95 70 6 71,95 78 6 70,875 II .

The British Petroleum Company

105 Vswap Vswap = B$ – S0B£ B£ B$ S0 Vswap = 150.000.000$ – (1.5$)(100.000.000£) = 0 Vswap Vswap = S0B£ - B$ Vswap = (1.5$)(100.000.000£) – (150.000.000$) = 0

106 أ . S0 S0 F = 1/S01 ب . جاتحن ج .

107 . . . . . . . Don M. Chance , Robert Brooks, An lntroduction to Derivatives and Risk

Management, (Thomson Higher Education by South-Western, Seventh Edition, Canada, 2006).

9. Gerald Gay, Anand Venkateswaran, The Pricing and Valuation of Swaps,

(Jhon Wilson and sons, 2010, Canada)

John Hull, Options, Futures, and Other Derivatives, 9em, Pearson

11. Michel Jura, Technique financière internationale, Dunod, 2e edition, paris, 2003.

12. Understanding interest rate swap math and pricing, California Debt and

Investment Advisory Commission, January 2007

13. Currency Swaps, sur le site :

xavier.edu/williams/centers/trading-center/documents/research/edu_ppts/05_CurrencySwaps.ppt; le : 06/07/2019, à 00:09