2 0 2 1 2 2 2 3
2 0 (contingent claim) 16 1973 ( C B O E ) 20-1 1973 1987 1987 ( )
514 20-1 ( ) Chicago Board Options Exchange Annual Report s, 1995 a n d 1997. 20.1 call option ( strike price or exercise price I B M 105 I B M ( p r e m i u m ) 1998 1 8 5 1998 2 105 I B M 2 2 0 105 / I B M 1 8 I B M 104.312 5 / I B M 105 I B M 105 2 2 0 I B M 108 105 108 = = 108 1 05 = 3 3 2 5 = = 3 5 = 2 put option 105 I B M 2 105 I B M
20 515 105 ( ) ( ) I B M I B M 1998 1 8 2 105 I B M 5. 25 10 / 2 2 0 I B M I B 105 104.312 5 =0.687 5 5. 25 I B M 96 = = 105 9 6 = 9 = 9 5. 25 = 4. 75 4. 7 / 5. 2 = 0. 905 = 90. 5 43 1 8 in the money out of the money at the money 20.1.1 ( ) 100 ( ) 2 0-2 I B M I B M ( N Y S E ) I B 104 5/16=104.312 5 / [ 1 ] I B M 80 120 5 100 30 2. 5 I B M 2 0-2 20-2 [1]
516 2 I B M 105 5 110 2 15/16 I B M 110 105 2 I B M 7. 5 5. 2 20-2 The Wall Street Journal, January 9, 1998. 20-2 20-2 (Long-term Equity AnticiPation Securities L E A P S ) 1 a. I B M 105 115 9 b. I B M 105 20.1.2 (American option)
20 517 (European options) 20.1.3 20-2 I B M I B M 1 : 10 105 105 I B M 105 1 : 10 10. 5 10 ( ) 2 I B M 120 105 1 1 0 12 10. 5 1 000 20.1.4 (Option Clearing Corporation, OCC) 100 20.1.5
518 500 2 100 100 30 1 700 225 ( A S E ) 300 2 0-3 20-3 The Wall Street Journal, January 14, 1998.
20 519 p c 100 O E X 500 1 040 1 050 (1 050 1 040) 100 1 000 37 35 2 20-4 20-4 The Wall Street Journal, January 9, 1998. 1982 ( C M E ) 2 0-5 62 500 68 0. 99 0.009 9 62 500 6 18. 75 ( I M M )
520 20-4 68 1. 22 20-5 0. 99 20-5 The Wall Street Journal, January 9, 1998. 20.2 20.2.1 100 I B M 110 10 / I B M 110 / 100 S T X S T >X 0 S T X ={ S T X S T X S T X 100 I B M I B M 9 0 1 0 0 11 0 1 2 0 1 3 0 0 0 10 20 30 100 1 00 1 20-6 2 0-6 14 20-6 100 14 114 S T X= 114 1 00 = 14
20 521 30 20 10 0 1 0 1 4 20-6 S T X ={ (S T X) S T >X 0 S T X I B M 2 0-7 114 14 100 114 20-7 20.2.2 I B M 90 100 10 9 / I B M 100 /
522 ={ 0 S T X X S T S T <X 2 0-8 100 I B M 100 100 100 100 100 S T 20-8 ( ) 1987 3 a. b. c. d. 20.2.3 I B M I B M 100 I B M 100
20 523 10 6 3 10 000 I B M A I B M 100 B 1 000 I B M 100 ( 10 100 ) C 100 1 000 9 000 3 9 000 9 000 1.03=9 270 I B M I B M 9 5 1 0 0 1 0 5 11 0 11 5 1 2 0 A 9 500 10 000 10 500 11 000 11 500 12 000 B 0 0 5 000 10 000 15 000 20 000 C 9 270 9 270 9 770 10 270 10 770 11 270 A I B M 100 B 1 000 C 9 270 100 10 000 9 5 I B M 1 0 0 1 0 5 11 0 11 5 1 2 0 A 5. 0 0. 0 5. 0 10. 0 15. 0 20. 0 B 1 00. 0 1 00. 0 5 0. 0 0. 0 50. 0 100. 0 C 7. 3 7. 3 2. 3 2. 7 7. 7 12. 7 20-9 20-9 B C A I B M B A I B M 100 B 1 00 100 115 120 4. 3 50 100
524 2 0-9 C 9 270 C 7. 3 I B M 1 00 I B M C A B C C 20.3 20.3.1 20-1 S T X S T >X S T S T + X-S T 0 = X S T 20-1 a) X = 1 0 0 I B M 97 100 97 b) X S T = 100 9 7 = 3 100 100 100 104 c) S T = 104 2 0-10 (Protective Put) 20-10 C S 0 +P 20-10
20 525 X=S 0 20-11 S T =S 0 S T S 0 S T S 0 2 0-11 2 0-11 (portfolio insurance) V. (Brane V. Roth) 40 40 40 40 40 t 40 60 6 60 4 t 40 40 40 40
526 / 40 40 20.3.2 covered calls 20-2 S T X S T >X S T S T + 0 (S T X) = S T X (naked option writing) 20-2 a) 2 0-12 c ) T X S T X b) X X 20-12 c ) c) X 20-12 1 000 I B M 100 11 110 6 I B M 5 10 I B M ( 100 ) 5 000
20 527 110 20.3.3 ( S t r a d d l e ) 20-3 S T <X S T X 0 S T X + X S T 0 = X S T S T X X S T =X a) b) 20-3 20-13 c ) S T =X c) 2 0-13 c ) 20-13 P+C X ( S t r i p s ) ( S t r a p s ) 4
528 20.3.4 s p r e a d ( ) (money spread) (time spread) X 1 X 2 20-4 20-4 S T X 1 S 1 <S T X 2 S T X 2 X 1 0 S T X 1 S T X 1 + X 2 0 0 (S T X 2 ) = 0 S T X 1 X 2 X 1 S T X 1 X 2 S T X 1 X 2 S T X 1 X 2 20-14 S T S T X= 110 X= 10 20.3.5 c o l l a r I B M 100 / 90 90 S X1 T X 2 110 20-14 110 110 150 000 140 000 10 ( 1 ) 1 000 140 ( 2 ) 1 000 ( 10 ) 130 ( 3 ) 1 000 ( 10 ) 150 10 000
20 529 10 000 20-2 ( Wo r l d C o m ) (David C. McCourt) 812, 308 5 28 64 812 308 64 812 308 2 (Morgan Stanley, D e a n Wi t t e r ) Elizabeth McDonald, WorldCom Director Uses Exotic Play to Hedge Stake, The Wall Street Journal, October 15, 1997. 5 I B M 90 110 20.4 100 10 000 10 X T S T X S T >X 0 S T X X X X S T
530 X X S T X X S T 20-1 C X/ ( 1 +r f ) T C+X/ ( 1 +r f ) T S 0 ( ) P ( 2 0-1 ) 20-1 put-call parity theorem 110 X C + (1 + r f ) = S T 0 + P ( X= 105 ) 1 7 ( X= 105 ) 5 10. 25 20-1 X C + (1 + r f ) T =? S 0 + P 17 + 105 (1.1025) 1/2=? 110 + 5 117=? 115 ( ) ) 100 ( ) S T 1 00 105 S T 105 S T 1 0 S T 105 S T 2 0-5 2 2 20-1 20-5 S T < 1 0 5 S T 1 0 5 11 0 S T S T 105 /( 1. 1025 ) 1 / 2 = 100 + 100 1 05 1 05 + 1 7 0 (S T 1 0 5 ) 5 1 0 5 S T 0 2 0 0 2 0-1
20 531 P=C S 0 + P V (X) + P V ( ) (20-2) P V ( ) 20-2 20-1 20-2 20-2 20-2 I B M 105 I B M 5 43 5. 25 I B M 104.312 5 4. 9 1 8 P=C+ P V (X) S 0 + P V ( ) 5.25 = 5.00+ 105 (1.049) 43/365 104.312 5 + 0 5.25 = 5.00+104.41 104.312 5 5.25 = 5.097 5 0. 15 20.5 (embedded option) 20.5.1 14 ( ) 20-15
532 2 0-15 45 6 7 20.5.2 ( ) 8 ( c o n v e r s i o n r a t i o ) 1 0 1 000 10 a) ( c o n v e r s i o n p r i c e ) 1 00 1 0 1 000 100 10 b) 950 10 95 10 950 c) 20-16 ( c o n v e r s i o n v a l u e ) a) b) c)
20 533 20-16 a ) ( ) b ) c ) A 8 0 8 0 1 0 1 0 B B a a B a a 2 0 2 5 3 0 5 0 6 0 0 1 250 10 B a a ( ) 8. 5 8. 5 967 967 9 7 2 1 255 ( ) 8. 42 4. 76 A 600 967 8. 5 972 5 972 8. 42 B 1 250 1 255 ( 5 ) 4. 76 1) 2) 3) 20.5.3 Wa r r a n t
534 [ 1 ] 20.5.4 L S T S 0 S T >L S T <L S T [ 2 ] a) S T L S T S 0 L L b) L S T S T L L L S T < L c) L L 20-17 [1] ( ) [2]
20 535 S 0 C S 0 C L P L/ ( 1 +r f ) T P S 0 C=L/ ( 1 +r f ) T P ( 2 0-3 ) L 20-3 2 0-17 a ) S T L b ) S T ( ) c L 20.5.5 20.6 20. 4 ( 22 2 3 ) 1985 ( L i q u i d - yield option note LY O N ) [ 1 ] Waste 1985 250 2001 1 000 9 Wa s t e 4. 36 [1] John J. McConnell Eduardo S. Schwartz The Original of LYONs: A Case Study in Financial Innovation Journal of Applied Corporate Finance, Winter 1992
536 10 40 (Bull certificate of deposit) ( 500 ) 100 7 (participation rate) 70 20-18 500 1 9 9 5 30 1996 20 10 (Keyport LIfe Insurance Co.) (John Rosensteel) (Petter Katt)
20 537 Bridget O Brian and Leslie Scism, Equity-Indexed Annuities Score Big Hit, But They Put a High Price on Protection, The Wall Street Journal, May 30, 1997. 1) 1 r f /( 1 +r f ) ( 1 r f /( 1 +r f )) =0.7 2) r M = 20-18 3) 1 1 r f /( 1 +r f ) C/S 0 C S 0 r f /( 1 +r f ) C/S 0 r f /( 1 +r f ) C/S 0 7 0 1 0. 7, 0. 7 r f /( 1 +r f ) C/S 0 r f = 6 50 1, 000 1 50 / 1000 = 0. 05 3 r f /( 1 +r f )=0.03/(1+0.03)=0.029 1 0.029 1/0.05=0.582 5 (r f r m i n )/( 1 +r f ) r m i n (bear CD) 500 6 9 r f = 3 50 1 000 0. 5? 20.7
538 (exotic options) 20.7.1 ( ) 20.7.2 (down-and-out option) ( k n o c k - o u t ) ( k n o c k - i n ) 20.7.3 ( l o o k b a c k ) X 20.7.4 (currency-translated option) q u a n t o q u a n t o q u a n t o 20.7.5 (binary option) 100 ( ) (RISK Magazine) 1. 2. 3. 4. 5. P=C S 0 + P V (X) + P V ( ) X P V (X) X P V ( ) 6.
20 539 7. (Chicago Board Options Exchange Reference Manual) ( M a rgin Manual) Black, Fischer. Fact and Fantasy in the Use of Options. Financial Analysts J o u r n a l, July-August 1975, pp. 3-20. From Black-Scholes to Black Holes: New Frontiers in Options. London: RISK Magazine, 1992. 1. 2 0-2 I B M 105 a. X= 100 b. X= 100 c. X= 105 d. X= 105 e. X= 110 f. X= 110 2. 6 S 0 100 6 X 1 00 C 1 0 10, 000 a. 10 000 100 b. 10 000 1 000 ( 10 ) c. 100 ( 1 ) 1 000 9 000 6 4 ( 8 ) 6 a. ( 100 ) b. (1 000 ) c. + 100 8 0 1 0 0 11 0 1 2 0
540 3. PUTT 1 00 100 1 a. 10 100 P U T T ( ) b. 4. CALL 50 / 50 4 a. 10 50 C A L L ( ) b. c. 5. ( ) - D / a. + b. (X+D) + c. a b - 20-2 6. a. X 1 X 2 X 3 X 1 X 2 X 2 X 3 b. X 2 X 1 X 2 X 1 7. X 2 X 1 X 2 X 1 20-14 8. ( J o n e s ) (Computer Science, Inc.) 10 000 40 / 40 000 35 000
20 541 45 000 a. A 45 3 b. B 35 3 c. C 9. 780 900 8 40 84 a. ( 900 ) b. ( ) c. ( ) 9 0 0 ( 840 ) 810 ( 840 ) 120 ( 780 ) 6 S T = 700 840 900 960 S T d. e. c - 10. 11. 12. 1 000 1 13. a. b. a c. 14. 105 1 I B M 100 1 I B M
542 a. I B M b. I B M 102 / I B M 115 20-1 c. d. I B M 15. 90 95 a. b. 16. 60 A c m e 2 62 A p e x 2 17. 20-2 I B M 100 1 18. X= 10 X= 10 9. 5 (X ) 19. ( ) 20. X= 100 X= 110 a. b. c. 21. ( J o e ) 400 / 20 40 ( S a l l y ) 390 15 a. b. c. 22. X= 50 X= 60 3 9 a. - b. c. 23. ( ) 53 24. a.
20 543 i. ii. iii. i v. b. 25 4 40 2. 50 5 ( ) i. 8.50 ii. 13.50 iii. 16.50 i v. 23.50 c. 1 000 40 2 i. 200 20 ii 200 25 iii. 250 2 i v. 250 25 d. X Y Z 40 2. 0 40 3. 50 i. 3 8. 0 0 3. 5 0 i i. 3 8. 0 0 3 6. 5 0 i i i. 4 0. 0 0 3. 5 0 i v. 4 0. 0 0 4 0. 0 0 e. A B C 45 4 A B C 55 i. 4 ii. 6 iii. 10 i v. 20 6. A B C i. B ii. B C iii. C i v. A B C 1. a. S T X =S T X=S T 1 05
544 = 5 S T = 9 5 S T = 11 5 / 0 10 / - 5 5 b. =X S T = 105 =S T = 5. 25 S T = 9 5 S T = 11 5 / 10 0 / 4. 75-5. 25 2. 100 ( 120 1 05 )=1 500 1 000 ( 12 1 0. 50 )=1 500 3. a. = 0 S T X (X S T ) S T <X b. = + =P S T X P (X S T ) S T <X c. d. 4. S T X S T >X 2 2 (X S T ) 0 1 0 S T X S T X S T >X 2 X S T 0 1 0 2 (S T X)
20 545 = 2 = 1 = 2 = 1 5. 6. 20-15 7.
546 8. 9. ( 0. 03 0. 005 )/1.03=0.024 27 50/1 000=0.05 0.024 27/0.05=0.485 4