cn Ac Av R Opon W Conol V U-LA LAO Aoc ofo of nnc pn of on n Bnkn onl Cnc Unv 64 C-nn R.c. p 6 wn l : 886--93939 85 : 886--93984 El A:lol@nccu.u.w COU-WE WA An ofo of nnc pn of nnc onl oun Unv of cnc n cnolo Juou R. nz c oun 8 wn l : 886-7-6 : 886-7-669 El A: lov@pco.co.w : 7/4/
cn Ac Av R Opon W Conol V U-LA LAO A COU-WE WA B on clo-fo oluon of pl opon w v pc of nl opon w lvl n connuou. uo w pov o pcl ccc of cll n pu opon. W plo pnon of l up n fo cll n pu opon un n po wnv ock pc ouc. o pccl pplcon w u cll opon w connuou conol v o vlu pc of c v opon l on wn ock Ecn fo 998 o 999. -pnn opon wo poff nflunc p of pc of unln v co ncnl popul n cn. On of p-pnn opon opon. k pc of opon woul u onl on pcf f pc of unln low on of lvl. n pcc opon v n fo n. Cco Bo Opon Ecn CBOE n w Yok ock Ecn YE o nouc & 5 n pu wn w -on po n l 996. on nl u wn w n nl k pc of $44.73 n Jul 997. k pc woul u o $39.76 on Auu 5 997 f pc of unln fll low $39.76. n 998 n C cu n wn u opon k pc woul u f - v clon pc of Un colconc Copoon wo cu co n wn ock Ecn E 33 fll low 9% of nl k pc $58.5 un f on f wn w u. nc opon nw vv n fnncl k l lu W ful o n nonou f n o pn lwk o fo lpful con n uon. An nn o ou.
. n Wl 997] n pcn of & 5 k wn w poc n cop v-à-v n &5 pu n lvl n voll cn. n Wl 999] lo pov clo-fo oluon fo opon w nl. Cn n n ] u opon k pc wll o pvln ock pc f opon ou of on. A clo-fo pcn foul n of ulv nol uon v un k-nul fwok. nl poff of opon w n n nl k pc u Cn n n ] follow: C { n... ] } n n pcc nl poff of opon o ofn C ] ] R... n ] > f n fo... w... k pc n... lvl; > > L > >. opon c n n cull op n l wol. Lo n Wn ] pov c clo-fo oluon fo nl opon w lvl n n p-c un k-nul fwok. pnon of l n up co wll pop of l n wvn n lo nv n pp. vl kn opon w f on fo n pl non of ulv nol uon 9. ffcul o clcul ccu cuulv pol of ulv nol uon w non n nc ccu pc of opon w n lo ffcul o on. uo clo-fo oluon of c v opon o no
u o fc u of lonol vl no lonol. n o o ovco pol ovon fo pp o u l connn cl o ppo vlu of opon o o k l connn cl conol v n on Clo ulon o on pc of c v opon. l connn cl w u n pp ulpl pl opon w lvl n connuou po l n o u. Acconl un nl o w v clo-fo oluon fo nl- opon w onon po l n o u.. pl opon. foul ul of nn n 994] n u 997]. n w u pl opon uln lock o v clo-fo vluon of nl opon w lvl n connuou po wc l n o u. uo w conuc on Clo ulon un clo-fo oluon of opon w lvl n connuou po conol v o vlu pc of n c v opon w lvl n n. An ouln of pp follow. W l ol n v clo-fo vluon of nl- opon n nl opon w connuou n con Ⅰ. n con Ⅱ w pn o pop of opon w connuou n cop cul un pc of opon w ul pc. con Ⅲ pov concluon of pp. Ⅰ. RC ARAL REE OO W u nc of unln pc c follown occ ffnl quon: 3
Q W w n > conn n conn po n ov n po ]. Q W n fo on-nonl n Bownn oon fn on fl pol pc Ω Q w Q po nl u o k nul pol u. vn ccoun B fn B B L p n po nvl ] l of po w <. poff of nl- own-n-ou o own-n-n cll opon n own-n-ou o own-n-n pu opon p follow: OC O ] n ν > C ] n ν ν ν ] n ν > ] n ν ν w nco funcon; > n. ν ll poff p of nl- up-n-ou o up-n-n cll opon n up-n-ou o up-n-n pu opon vn follow: UOC UO ] ν < UC ] ν ν ν ] ν < U ] ν ν ν w < n. n o o v vlu of ll p of nl- cll n pu opon w po l n o u w f pov follown o: 4
5 o. Au W u n > n w v ] n u u u u u 3 ] n u u u u u 4 ] u u u u u 5 ] u u u u u 6 w cuulv pol of v nol uon w zo n n nnnou colon coffcn. W pov o n Appn A. Un o w cn fowl v pc of ll nl- opon own n o. o. L OC UC n U pc of own-n-ou cll own-n-n pu up-n-n cll n up-n-n pu w po wc l n -o-u pcvl. n w v OC 7
6 UC U 8 w n ln ln ln B pu-cll p w v follown lon: OC C C U UO UC C UOC O w ] ] C ] ] 9
7 W pov o n Appn B. Un fc ] ] l l n ε ε w ε n nol no vl w know wn ppoc pc of p of opon wll co opon w po n qul o o u. kn own-n-ou cll opon n pl wn ppoc w v ] ] l OC ] ] wc ul of Runn n Rn 99]. ow con cll opon w lvl n connuou w po l n o u. poff p follow: R C ] ] > n f fo... o quvlnl R C ] > > n n w... n > > > > L. Coponnl poff p of pu opon w lvl n connuou w po l n o u follow: R ] ] f > fo....
ll w v R ] w... n > > L > >. fo w cn plc cll opon w follown n :. uc on un of Euopn cll opon w k pc.. uc on un of Euopn own-n-ou cll opon w k pc... fo c. 3. o ll on un of Euopn own-n-ou cll opon w k pc... fo c. n w w cn plc pu opon w follown n :. uc on un of Euopn pu opon w k pc.. uc on un of Euopn up-n-n pu opon w k pc... fo c. 3. o ll on un of Euopn up-n-n pu opon w k pc... fo c. Conqunl w v follown ul: o 3. L R C n R no pc of opon w lvl n connuou w po l n o u pcvl. > > n fo.... > n > fo.... -f pc of nl opon R C ] ] OC OC R ] ] U U 8
w OC f o own-n-ou cll w k pc n lvl. U f o up-n-n pu w k pc n lvl. OC n U vn 7 n 8 pcvl. cll o pu opon w po l n o u cn v upp oun o conol v of cll o pu opon w c pcll wn n c n nc wn n wo cn ll. Ⅱ. UERCAL AALYE O REE OO Ccc of R Opon w Connuou R w cu pop of cll opon w connuou. Con on--u cll opon w nl k pc. k pc wll u f clon pc of unln ock fll low 8% 7% n 6% of nl k pc. W cop pc of opon w 3 lvl n po of on on n on o pln vnll cll opon. ul own n l Ⅰ. o l Ⅰ o ccc of cll opon l o n Euopn cll opon. vlu of cll opon ncn funcon of ock pc k-f n n voll of ock un. n on fv pop unqul n cll opon: vlu of cll opon ncn w uon of po. Un lvl low k pc wll v vlu fo cll opon. 3 u o o pocon ow ol of cll opon vlu of cll opon w connuou lw n vlu of pln vnll cll opon. 4 Bcu cll 9
opon ncn funcon of po opon w connuou cn v upp oun o conol v fo cll opon w c. 5 n c of vlu of ock pc n lvl n low voll of ock un pc oun fo cll opon w c wll ll. o pl wn ock pc k-f voll of ock un n k pc 5.5.3 n 987 pcvl pc oun of cll opon w c c of on-on onon po 4.8644.8643]. W now nv pop of pu opon w connuou. Con on--u pu opon w nl k pc. k pc wll u f clon pc of unln ock ov 5% % n 5% of nl k pc. W cop pc of opon w 3 lvl n po of on on n on o pln vnll pu opon. ul pn n l Ⅱ. l Ⅱ ow ccc of pu opon lo l o pln vnll Euopn pu opon; nl vlu of pu opon cn funcon of ock pc n k-f n ncn w voll of ock un. Aonll pu opon v follown pop: l o cll opon vlu of pu opon ncn w uon of po n n vlu of pln vnll pu opon u o o pocon ow ol. vlu cn v upp oun o conol v fo pu opon w c. Un lvl k pc wll nuc vlu of pu opon. 3 n c of low vlu of ock pc n lvl n low voll of ock un pc oun fo pu opon w c wll ll. o pl wn ock pc
k-f voll of ock un n k pc 85.5.3 n 55 pcvl pc oun fo pu opon w c c of on-on onon po 6.546.549]. l Jup of R Opon nc w cn plc opon w opon l o opon opon lo v pnonon of l up wnv ock pc ouc. Un cn ul of ffnon w cn v l of opon. ul pn n follown o. o 4. l of cll opon n pu opon follow: C R OC OC ] R U U ] w B A OC B A Y U Y ] ] ] p π A
] ] p π ] ] p ] ] p π π B ] ] ] p π ] ] p π ] ] p ] ] p π π Y l up cn occu n wn po. f ock pc ouc fo l woul co follown pon: C R OC OC ] R U U ] Bcu k pc of OC n OC o U n U ffn OC OC n U U wll no qul o zo. A ul ] u l wll up f ock pc ouc.... o pl con wo c follow: On--u cll opon k pc wll u f clon pc of unln ock fll low 87.5% 75% 6.5% 5% n 37.5% of nl k pc 8. voll of ock un.5. On--u pu opon k pc wll u f clon pc of
unln ock ov 8 7 7 7 4 7 n 6 7 of nl k pc 35. voll of ock un.3. Bo opon v po on. l plo n u n pcvl. pnon of l up n o c. l up ppn wnv ock pc ouc. o cll opon wn ock pc ov vo of l l o l of pln vnll cll opon. owv wn ock pc fll n ouc u o k pc n u o nw low lvl l of cll opon wll up o lvl. o pu opon wn ock pc low low vo of l l o l of pln vnll pu opon. vl wn ock pc o clo o u o fc k pc coul u o nw lvl f ock pc cull ouc pu opon o vlul. oc l of pu opon wll nc n vn co pov. Af ock pc cull ouc k pc u o nw lvl. Conqunl pu opon n v pln vnll pu opon n l up o low lvl. o kn cll opon n pl f nu ock pc ouc l of cll opon follow: C R l OC OC l ] ] owv l ] ] > ] Copn n w cp c ock pc 3
n l ffn fo l fo. A ul ovou l wll up n po ] wnv ock pc ouc low of cll opon. ucl Rul of c of Ac Av R Opon n pcc opon u c v of ock pc. owv u o pol u of lonol uon no lonol c clo-fo oluon of c v opon o no. o on w u opon w connuou po conol v fo on Clo ulon o on f pc of c v opon. o on Clo ulon w k cll opon n pl. W pon nvl ] no n unvl of qul ln n l pon pon... n. W n v ln ln ε... n w ε... n ncl n npnn n nol no vl. o ul p... w co nu vlu of ock pc un po. f nu vlu low l lvl fo l... n vlu of conol v pl cll opon ] C Conol ] ] p l o vlu of c v cll opon uppo n on n fo c pon pon. W v n. 3 n c v vlu of ock pc copu on pon pon... n. ll fo ul p w co nu c 4
v vlu of ock pc un po. f nu c v vlu low f lvl fo f... n vlu of c v cll opon ] C R p ] ] A ul vlu of c v cll opon w conol v R Conol R C C ] C R Ĉ f w R C copu on. W cn lo u nc v f popo Bol 977] n opon pcn cn pfcl nvl col. n w v p o copu opon vlu. B on ov o ou pcl pouc c v opon l on E fo 998 o 999. conon of c v opon own n l Ⅲ. o l w nu of c l fo o nn n nvl wn n wo cn onl on. Conqunl kn of opon w n c cn u opon w connuou po conol v n on Clo ulon o vlu f pc w ll n von. un 998 n 999 w u R Rpuc An po of k-f n wc wn 4% n 5%. nucl ul fo ulon uz n l Ⅳ. o l w cn n von of ulon ll un conol v. nwl cl kup of opon n wn wn % n %. 4 kup ul fo ncon co n ulon con.. no llow o u pu opon n wn. 5
Ⅲ. COCLUO Un nl o w pov clo-fo oluon fo p of pl opon n opon w connuou. W lo ow o pcl ccc of cll n pu opon. Bo of cll n pu opon ncn w uon of po n vlu of pln vnll opon u o o pocon ow ol n cn v upp oun fo cll n pu opon w c. W lo pov l of cll n pu opon n nv pnon of l up n n cll n pu opon un ll po wnv ock pc ouc. nll clo-fo oluon of opon w connuou po cn u conol v n on Clo ulon o copu f pc of c v opon. o nucl nl w u c v opon l on E fo 998 o 999. ulon ul ow kup of opon u n pcc wn % n %. kup cu ncon co n ulon con. 6
ABLE Ⅰ c of ln Vnll Cll Opon n R Cll w 3 R lvl n R o of On on n on 3% 5%.5. 7 R o R o On 3 On on on on on 876 9.7863.8476 876.4785.57 857565 6.47 8.6997.58 85 857565 7.37 9.37.859 987 7.7947 8.755 987 8.439 9.446 876 4.978 5.89 876 5.766 6.58 857565 4.33 4.76 4.8774 3% 857565 5.5 5.553 5.853 987 4.579 4.66 987 5.373 5.66 876 4.8644 4.967 876 6.77 6.757 857565 4.864 4.8643 4.933 5 857565 6.769 6.77 6.434 987 4.8643 4.95 987 6.77 6.66 876 8.589.48 876 9.57.79 857565 3.563 7.589 9.633 85 857565 3.7675 7.73 9.7474 987 5.7593 7.3 987 6.457 7.996 876.77 5.4 876 3.5686 6.789 857565.796.4564 4.338 5% 857565.6369 3.33 5.84 987.97 3.539 987 3.66 4.385 876 3.6 33.4457 876 33.635 34.48 857565 3.9 3.84 33.86 5 857565 33.78 33.37 34.89 987 3.6 3.7688 987 33.37 33.86 85 5 85 5 3 8 7 6. o pop unqul n cll opon: 3 vlu of cll opon ncn w uon of po. Un lvl low k pc v vlu fo cll opon. 3 u o o pocon ow ol of cll opon vlu of cll opon w connuou lw n vlu of pln vnll cll opon. 4 Bcu cll opon ncn funcon of po opon w connuou n pln vnll cll opon cn v upp n low oun fo cll opon w c pcvl. 5 n c of vlu of ock pc n lvl n low voll of ock un pc oun of cll opon w c wll ll. 7
ABLE Ⅱ c of ln Vnll u Opon n R u w 3 R lvl n R o of On on n on 3% 5%.5. 7 R o R o 3 On 3 On on on on on 55 6.549 6.668 55 5.44 5.363 5 6.54 6.549 6.7554 85 5 5.43 5.449 5.456 55 6.543 6.863 55 5.46 5.5634 55 9.638.56 55 8.6858 9.55 5 9.354 9.8.897 3% 5 8.4499 8.8934.949 55.74.746 55 9.33.473 55 8.99 8.8799 55 7.393 7.9977 5 4.987.477.89 5 5 4.464 9.459.35 55.886 3.746 55.76.54 55 3.49 4.97 55.53 3. 5 3.79 3.484 4.8336 85 5.69.64 3.548 55 3.574 5.464 55.98 4.863 55 8.39 9.8668 55 7.79 8.765 5 6.955 9.99.36 5% 5 5.8763 8.56.9 55.6.87 55 8.8467.687 55 7.48 7.9883 55 6.347 6.8739 5.4.33.6667 5 5.4 8.89 9.458 55.855 3.554 55.4836.359 85 5 85 5 5 5. pop of pu opon : 3 vlu of pu opon ncn w uon of po n vlu of pln vnll pu opon u o o pocon ow ol n cn v upp oun fo pu opon w c. Un lvl k pc wll nuc vlu fo pu opon. 3 n c of low vlu of ock pc n lvl n low voll of ock un pc oun fo pu opon w c wll ll. 8
ABLE Ⅲ R Conon of R Opon on wn ock Ecn Co n E R Conon k pc woul u f - v clon pc of 33 on 57 E fll low 9% of nl k pc $58.5 un f on f wn w u. k pc woul u f - v clon pc of 33 on 5 E fll low 98% 96% 94% 9% 9% of nl k pc $8 un f on f wn w u. k pc woul u f - v clon pc of 33 on 53 E fll low 8% of nl k pc $57 un f on f wn w u. k pc woul u f - v clon pc of 3 on 57 E fll low 8% of nl k pc $95.5 un f on f wn w u. k pc woul u f - v clon pc of 373 on 58 E fll low 95% 9% 85 of nl k pc $58.5 un f on f wn w u. k pc woul u f - v clon pc of 33 on 538 E fll low 85% of nl k pc $8 un f on on f wn w u. l ow of opon l on E. opon u c v of ock pc n v ulpl lvl. 9
ABLE Ⅳ ucl Rul of Ac Av R Opon Co n u u ocl.4. 5 E c Voll c kup c kup 57 998// 6.43 5.36% 3.878.79 7.7 % 4.959.8 6.56 % 5 999/4/8.5 43.5% 7.636.55 5.3 % 7.967.55.65 % 53 999/5/7 3.68 45.93%.363.6.48 %.593.9 8.5 % 57 999/6/9 4.83 49.7%.9984.9.97 %.3975.9.78 % 58 999/6/4 5. 45.3% 3.3833.65 3.64 % 3.64.65.4 % 538 999//.87 49.46% 7.945.44.96 % 8.6.4 9.5 % nucl ul on of opon n l Ⅱ. n von of on Clo ulon. o u pon no 7 unvl of qul ln. kup coun u c - c / c%. o l cl kup of opon n wn wn % o %. kup ul fo ncon co n ulon con n wn no llow o u pu opon o.
URE l of R Cll w v R Lvl n -on R o.8.7.6.5 l.4.3.. 3 4 5 6 7 8 9 ock c 8... ] 76543]... ] 76543].5 v. 5. 5 5 po on.
URE l of R u w v R Lvl n -on R o.4. -. l -.4 -.6 -.8-3 4 5 6 7 8 9 ock c 35... ] 45678]... ] 5 5 po on. 45678].5 v. 5.
AE A oof of o Au u W c n > w W n fo on-nonl n Bownn oon on fl pol pc Ω w flon n. fn v W n W W u v. Acconl w v c E p w n { c }. L pol u quvln o uc Ron-ko vv v v p vw p v B nov o poc W fn W W v follow n Bownn oon un pol u. o flcon pncpl of Bownn oon w v c E p v v pv E p v v c nc c n { } { } { c } Conqunl c 3
4 p p c v v E v L pol u R on Ω fn Ron-ko vv p v v R. n poc R W fn v W W R n Bownn oon un pol u R. nc v W R n w on c p c v R v c v v p n w c v c v v p w cuulv v nol uon w n vco n nnnou colon coffcn. L ˆ n n n c c u u u c p ˆ ˆ ˆ A ul w v c c c c u u u c u u p Bcu follow
5 u u u u u p copl poof of 3. o pov 6 f no W v W v v v fo w v follown pon: u u u u u p ll u u u u u p A. n un A. w on u u u u u p copl poof of o.
6 AE B oof of o Un k-nul pol u Q -f pc of own-n-ou cll opon follow: ] > Q n E OC { } { } Q Q E E w > n n pcf n Appn A. Conqunl w v { } Q Q W W E E p L pol u fn Ron-ko vv p v vw Q. n W fn v W W n Bownn oon un pol u. fo { } { } Q E E > n > n > n ln ln w W n o n n npnn of
7 fl. Conqunl { } Q E > ln ln Un 3 w cn on { } Q E Coponnl w lo v { } Q E A ul OC. n follown pocu un 4 o 6 w cn v pc of UC n U. pu-cll p of OC n C follow: ] > Q n E OC ] Q n E ] { } Q E ] Q n E C C ll w v U UO UC C UOC O w C n fn n 9. copl poof of o.
EOE. nn n 994] u nl pon n u 997] u..e. ppoc o vn clo-fo oluon of pl opon; owv no v pc of opon. pp pov c w un pl vluon ppoc nl o n off n no occ pop of pc poc of unln.. l pnonon lo ppn fo pu opon. 3. w cn u o p o k n. 4. Alnvl w coul u pl voll o copu c v opon on E. owv w no on opon fo cu. u w onl u ocl voll o copu pc of opon. 8
REERECE Bol.. Opon: A on Clo ppoc. Jounl of nncl Econoc 4 977 pp. 33-338. Cn W. Y. n. n. Anlc of R Opon. Jounl of vv pp. 59-7.. n R. Wl. Vlun & 5 B k Wn w oc R. Jounl of vv 997 pp. 99-6.. n R. Wl. R u Opon: Vluon Rk Ccc n n Applcon. Auln Jounl of nn 4 999 pp. -. nn R. C. n... l B Opon. Jounl of nncl Ennn 3 994 pp. 53-74. u C.. -pnn opon vlu. Jounl of uu k 7 997 pp. 667-688. Lo.L n C. W. Wn. Vluon of R Opon w ulpl k R n R. Jounl of uu k ocon. Runn. n E. Rn. Bkn own B Rk 99 pp. 3-35. 9