A Bs h S D M. Chc Ths A. Hs Wg L J Muhusw Sb 9, 04 Absc s w-kw h k cs f s uc vs h v c h v s. W s h v f s wh Bck-Schs-M cg sg v, w wu bsv ss, skws, sks f h ghs us us. Wh s hc ssb s h b, s fsb cc. s v ffcu c h b wh ss s fc k fcs, s s c bv. W c s h w bu f hs ffc bu 8% f h bsv s. K ws: Bck-Schs-M, cg, v, v, v s, cu fc, s JEL Cssfcs: C8, C63, G3 Th uhs, scv, Js C. Fs Ew Ch f MBA Sus Pfss f Fc, D f Fc, Lus S Uvs, 909 BEC, B Rug, LA 70803, 5-578-037, chc@su.u; sg Asss Pfss f Fc, M Ahuj Cg f Busss, Cv S Uvs, Euc Avu, Cv, OH 445, 6-687-3786,, hs3@k.u; Ws Fcu Fw f Fc Pfss f Mhcs, D f Fc, Okh S Uvs, MSCS 56, Sw, OK, 74078, 405-744-585, w@h.ks.u; Assc Pfss f Fc, D f Fc, Cg f Busss As, K S Uvs, P.O. Bx 590, K, OH, 444, 330-67-6, juhusw@k.u. Ths ws s h 3 Au C-FDC-Hus Dvv Scus Rsk Mg Cfc, h R/Fc 03 Cfc, h HEC M 03 Mhc Fc Ds Cfc, h 03 OsMcs Cfc, h Suh Fc Assc, h Assc f Quv Fc, Bbg, b, Lus S Uvs, N Uvs f Sg, h Uvs f A, NYU-P. Th uhs c hfu cs suggss f Rb Bks, Jsh Zh, Ysg T, P Lck, H B-Au, Pu Kuc, Ph B, Jh Twbg, Psks Gbs, Tj Puh, Jsh Lgh, Mk S, Ov H, Sv Muzz, Rb Jw.
A Bs h S A s s h chs vhc f bgus. H Mv (P, 85). uc O cg s csuc wh h bjcv f vg h c f gv. Th s wk h s h Bck-Schs-M (BSM) (Bck Schs (973), M (973)), whch vs h vu f fcss k hugh h us f hg f bg-f cs. F ug ss h ks csh s cus cg css ug h s f, h vu s b h c f h ug, h xcs c, h skf, h x, h v f h ug. Of hs fv us h, h v f h ug s ubsvb. S f h ws uc, ws cgz h h h f vus f s v, c v h css. Obsv k cs f c s cu h b s h bck u s f h ubsv v f h ug. hs, cu f h v f h ug h ws bg us b k cs s h c s. Y hs css v c g: s h s ug wh h s x h s v. Ths sh f v css sks hs c b kw s h v s, wg h U-sh h s f bsv. s w w-sbsh h h ss s vs wh sc bh sk cs x, h cb ffcs f whch f kw s h v sufc. Y hs s s uzzg h. 3 Th fs vss f h w b Lé R (976) Schs T (978). E s css ssu h hs su ws fc f bsv ccucs h, such s gh ccu f h sck cs w schus f h w s g vu h h c wu b v sv c. Th c ch k b css jus f uqu vs hs b k vg v, s css wghg h vs b g vu, ss, h s vgs. Ths cs v s ss c h wgh s v. 3 Mhw v gs s f s s, T v k bu v ss s schzhc, (995,. 4).
Bcus h v ss h v f h ug, whch us b f b uqu, s h ff b sk shu hv h s v. 4 Rsch g xc hv s ucv h fc h s, f s, s ss. S skw s s sb sk. Whh h sh bw v xcs c sbs s, skw, sk, v f h hz s c h h s u vs f h ug ss. Th bvus x h hs b scuss xsv h u s h h s fc k ssus f f. Acu cs h k c h s s hs ssu, bu hs ssu s c fc s. Ah x s h vs f h ssc css fw b h ug cu b h suc f h v s. hs, w scb h x, s h bss f s x. Sus s fc ks. f f h ssus f h BSM, cu cs kw v cuus, csss g, wu h b v s? u ss h h vs f s wh ff sks wu qu h kw cs v us c h s h fs c. W shw h h hs sg xc su s u: v f vss c s ccc wh h Bck-Schs-M usg sg v, h vs css sks s ws v s qu b. Rkb, h s h f f ss, skws, sks h g sb h s bsv cc usg cs f ks h f f fc. W s shw h hs s uc h sh h u f h, whch s css wh c bsvs bs cu k cs. Of cus, hs su s uzzg, f shckg. Hw c b h c c wh kw v h b ub bck h v u f h c? x b b f u, h hs b susg bsc f h cs s f hw v s b. W w shw h h sh hg f svg f h v c kb ff vs f s h v b sk bu hv h cc ffcs. W s shw h h b bcs v ffcu cgz f h k 4 s vs css, ss kw s h sucu f v, cu gc hs fc. Th qus h v b cs v h f f h. Ths ssu s cu ff vs css ff hzs.
fcs h cus s s b c u hs, whch, f cus, s h s x f h xsc f h s. W k c h hs h buks h s. s qu g bv b v b h f k fcs h cu cg s. Y, s c h h b f h s cgz h b f kwg. A bvus qus s, hf, hw uch f h s s ccu f b hs b? W cuc c ss f h h w bu f hs ffc s 8% f h k-bsv s, bu h f s s s s, hs ffc c b v 90%. W x s ssb xs sus bu u f h hs s b wh c fx. Th f h s gz s fws. Sc w vw h xs f h v s h hv h u. Sc 3 vs f scfc f h b scuss f h kw chqus f vg vs h v s. Sc 4 scbs u cu scfcs vsgv. Sc 5 ss u sus, whch cus uc fgs bu s c ss v h 004-00. Sc 6 cs u ccuss.. Pssb Exs f h S Fgu uss v s uc b h csg sk cs f B c s h Chcg B Os Exchg Ju 8, 03. Th s x Fbu 6, s h hv bu h g. 5 Th sck c s $54., h sk-f s 0.05%, bs x -h U. S. Tsu bs. Th cs k f h CBOE s wb s h cs f busss. EB s vs s hs Ac c s ffcv Eu c s. Th s s c sc gh b f s sk. g, w w us h s s u bu s s h hv b bsv. A c s, u sus w g sks skws, hs vs w b s wh v. Obsvs f v ss hv vk ub f ssb xs csb c wk. Much f h wk hs fcus fg sh fucs f h s sufc ccu s f h v f s wh 5 A f u sus w fcus c s. Th v s s f csuc wh u s cb f c u s. Th fcus f u s bs sg f us f h Bck-Schs-M f Eu c s h c f fc ks. S bs w s wh us. 3
sks xs cu. 6 Ou s ffs. BSM w, h xsc f s s h f ccug f h ffcs f h c f h ug, h xcs c, h sk-f, h x, h v, h c s wh shu b. 7 Thus, h s fc ccu f h ffcs h c. Th fc s, hf, bsb h v s. F x, U- sh s suggss h f cg h fv s fcs h ff cs, s wh h hghs ws sks s xsv h hs. Such x s css wh bg-f cg BSM w. Wh cuus csss g, c c c h h s ug. Thus, fc BSM w, sg c b v ss xsv h h h s ug. Ohws, h wu b bg u.. M Assus Pvus sch hs ssu h h v s s u v f f h s ssus. Ju csss scuss Rubs (994), M (976), Bs (99), Ds Su (999), wh schsc v s s b Hu Wh (987) su b Hs (993), Rubs (994), Dus, Fg, Wh (998), hs. sg, c su, Bksh, C, Ch (997) f h cg schsc s s, schsc v, schsc v wh jus s h s, g u sg v. Th ssb f h ffc f - s hs b s b C Su (996). Th ffcs f sc css (P, Rub, S (999)), sc ck sz (Ds Mhw (009)), bug ssu s bg (B Wh (004), Shu, P, L, Wu (00)), bhv (g (009)) hv s b cs. A w-cc bf s h uusu hgh vs w-sk us s f f csh suc, s b Rubs (994) bc fwg h csh f 987. F, h s h h ususg cs h s skw c su wh s c b, bu v s b f h, s us b Shw (998). H uss hw cs v 6 Sh v fucs cs, bcus h v cs h c qu f s h gh cu b, bu whch cu c. fc, s c f s qu cs, b sg h c c, bu b qug h v. A vs b s bu 0, g h h c h s s $0 bu s b sg 0% s h v h cg. 7 Rfc Bck-Schs-M w s w whch f h ssus f h cc, h ws, fc k. Hc, cs wu cf h. Of cus, h k ssu h s h h v s kw g u b vss. 4
b h cs sc f vc uc skw wh h v s bck u f h BSM. Th s s bv h hs xs cc. Y, h s s bv h cu fcs cu v s f h v. f cu fcs hv sgfc fuc h v, s ffcu h c f hs cc ss f h s., s w shw, h cs f hs ffcs wh cu s ks h b v ffcu c.. Cu Css A h ss sc f cu ffcs v s s Hsch (003), wh shws h su s h us c hv sgfc c h v. H css fss f qus, h xsc f b-sk ss, -schus cs f h ug. Ths sgh ss f c us c sgfc v v s. Ahugh Hsch s su s bb s cs us, h ffcs sgfc. Hsch s fcus s h --vbs bs h wu c bs us. cs, w ssu h us cc su fcus h chcs f hw us cv uus, kg ccu cvgc c, h sg, h -fg gh us. sh, w ss ssu h ks fc h ss h h BSM ssus h s c ccg hs bu h su csss us wh h s f hc kwg cu cbs. Th u v s kb v f scusss f cu s. F x, gv h h s c, cs-f su, ss f v ss subjc c scf b h us. Ths c s s scf xc h u. F sc, C Fgwsk (993) scb h css f ccug v s svg h cg f h v h ss h k cs qu (. 659). Lkws, Rubs (985) s f h h Nw-Rhs h cvgs quck (. 460). Chbs Nwkh (00) s h v c b s ccu usg v sch chqu (. 98). O fw sus xc scb h c qus. F sc, Lé R (976) qu h uc sch cu v su c wh ± $ f h s k c. Schs T (978) uz v cu h h wh us chg h s b ss h %., h s f 5
sg ss vs, whch qu b v fg chqu. Th vwhg j f s k f hw h v s v. 3. F Scfc f h Pb Th Bck-Schs-M fu s gv s wh c SN( ) K N( ) ( S / K) ( ( / )) (), whch N( ) ss h cuuv s fuc, c s h c c, S s h cu k c, K s h s sk c, τ s g x, s h cuus cu cs kw f s, σ s h v f h sck s u, whch s f h uz s v f h cuus cu u. Nw c M s h c f h s bsv cv qu k. Sg h c h k c, h v s h c su : wh c SN( ) K N( ) M ( S / K) ( ( / )), wh s h v, f s h v h fcs h k c qu h c. Of cus, s w-kw h s ssb c sv () f h v. 8 S schs hv x c ssus v cs-f xs (B Subh (988), Chc (996), Chbs Nwkh (00), Bh, Chsfs, Sk (996), Hbch (004), K (006), C M (996), L (005)). 9 Cs-f xs usfu ssh ggc cs bu hv bc ss cc g sc sch g bcus f h cs s f cus. 3. v Tchqus () 8 A c b Gh (0) shws f h h Bck-Schs-M s bg css f fucs f whch sus c b s fu. 9 S f hs chqus c b cs v h h us sg s qu s guss. A f cus, cu ws v chqu f h c cs-f x. 6
v hs v ccu sus b kg s v f ss, gussg h vu f h fuc h s v, gg w s, sg h css v, u hfu cvgg h f su. Cs h h s, f h v. Ths s ucs vu f h, c( ). Wh h bsv k c f h s c M, h ffc bw h k c f h s c( ) c SN( ) K N( ) c M ( ) ( ) M ( S / K) ( ( / )) ( ) wh Ths v chqus g vv h us f -fg cu f h cg qu, c( ) - c M = 0. Th cu gh sv hs b w ssss c qus f busss s f cvgc. Fuh, h c v, ccb, f ccug h w fuc h s f h v. As, s s h vv ccus f v f qu bqu h fg chqu. A c f hs s h h sc hs vk h v c f h cs f hs chc such fcs s sg s. W w shw h hs cu css hv sgfc fuc h xsc sh f h v s. Th b f hc kwg s wh -fg hs, fg s c b f sus f hcs cu scc. Ous f svg f h v, hwv, -fg bs v c fc g. 0 Thus, ususg, h hs b uch svg such bs h fc u. Kz (99) s w hs f vg h v, h Nw- Rhs h h bsc h. Bw (990) Chss (997) h bsc h. Oh w-kw fg hs, hugh h fc u, cu h sc h, h gu fs fs s h, h Dkk-B h.. (3) 0 Fg h f u c vs cs s -fg b h ss c fc. Ms fc bs cvgc, hwv, vv vvs. F x, cvgc ssus s svg f h b c, c sch b Muhusw Hs (0) suggss h h b gh cvg. sg, h gu fs chqu hs b cuf bs f c Bb hcs. S Chb (999). Rgu fs s scuss b Fg (0), bu u kwg hs b c swh h fc u. Dkk-B s us b Mb s h fu f. 7
Pbb h bs kw -fg v chqu s h f Nw- Rhs h. Gv s ws us, w x s. Ax B, w w v fs x f h v. W h us h x x h bhv f h Nw-Rhs h. Th fs x c b uc h fwg quc qu: q q q 0 0 0 3 K K S q S K 3 K Of cus, h su s w-kw s q q S S c M 0 q q 4q q 3 q S K S K c c M M S S K K S K S K S K. (4) Th g s gv b S K S K c c M 0 S S K K S K S K S K, whch s h su s b C M (996). N h h s c b S K sv s w wh q < 0, whch s quv S K S K c c M M 0 c M, s gv b S S K K S K S K S K. Chss (997) ss h u bs wh h bsc h h us shs us fs h, kw s h Nw-Rhs h (. 330). 8
sg, hs h su hs b cs vus sch. Th uc x s h su F( ) SN ( S,, K,, ) K N ( S,, K,, ) c 0. (5) Th Nw-Rhs h s gh h s sv hs qu usg h fwg css, x x Fx ( ), F ( x ) wh chc f x 0 s. Ev f F(x) hs vvs vwh, hwv, h Nw-Rhs h. F x, Nw-Rhs s cvg f h s fuc, F(x) = x 3 x + wh x 0 = 0. Chsg g sg s ssu f Nw-Rhs. Ev wh sg g chc, h c f F(x ) F (x ) c sw cvgc cvgc h wg. F x, f h s xss, F(x) = s x x/, sg f x 0 = s h gs sv, sg f x 0 =.0 s h gs gv, sg f x 0 =.0 s gv f, sg f x 0 =.05 s sv f. Thus, sgh chgs h sg c c ff sus s css, sus. 3 Th fc s f h fuc F gv b f M (6) f S, K (7) whch ccu wh h 0,, 0. Ths fu ws f f scv b Ms-Kh (98). W x s s fuh. f 0, h h w css cs: h () f < < 0 wh f S K S, whch ccus wh 0 () 0 < < wh K f S K S, whch ccus wh 0. Whu ss f g, w K k h sc cs f scuss. Thf, F 0 v 0. f 3 Th gh cgz hs ssv cs css s chs h cs. Rc suvs f cc fc cs v b Hsh (99) B, Ss, Ss (006). 9
f, h h s w css: h () f 0 f wh f S K, () f wh f S K. h cs, w hv F 0 v. f F Equ (5), w bu h Nw-Rhs h wh x0 f f h xc fu gv b h s f h quc qu. W hv h vg v, F F S( ) 0, F wh fucs f h v wh ( ) ( ) ( ) ( ),. f x su xss, h h su s uqu b h sc sv vg. Ths su ucs h cvgc ssu f h Nw-Rhs h s : f h gh cvgs, us cvg h cc su. Ths sus f s h fwg h. Th. L b h fc f h v f h Bck-Schsf M fu. Th w chs h sg x0 f Fx ( ) 0 W hv x x. 0 F ( x ) () f 0, f h Nw-Rhs h. 0, h w hv x x f. Thus, h Nw-Rhs f f h vss h v. v, x () f, h f cvgc s quc v ( x ) ( ) ( ) ( ) f x. Th gh s cvg h 0, h w hv x x f. Thus, h Nw-Rhs f h uss h v. Th gh s cvg h v, x, h f cvgc s quc v 0
( x ) ( ) ( ) ( ) f x. () f 0 f, h h Nw-Rhs h uss h v. Th gh s cvg h v cvgc s quc v ( x ) ( ) ( ) ( ) x. x Pf f hs h s v Ax A.. 4 f x. Mv, h f Th gh sf c gu cvgc s w chs sc sg Th vss uss u h cvx f h BSM fuc h v. N h s ssb h h f h Nw-Rhs h ucs sw cvgc squc f h v. Th cvgc cs h h gu h h f cvgc s quc. Wh w hv s g w f vwg h b, h cvgc cs c b sf f sc css. F x, f ( ) 0 cs (), w c c h x f b h cvgc f qu. Th c s u hc vv wh h v. cc, cvgc s bh css u h sc csg csg s. f v. f f, h w hv x 0 = x f, h sg s h f w sc ff sg s, h w wu hv h x 0 f x, whch cv h h. F h fs cs, w hv x > x 0 0 x. Thf, h w ssbs f h c f x : () wh h fs s x s x f f, w b h s su s h h; (b) wh h fs, w hv x < x c b c h s f. Thus, h Nw- Rhs h s ccusv uss x f f s. Th s h ccus f h sc cs, x uss x f s, whch s h s su s f 0 f cv u h. Th Nw-Rhs h c s f f h ss. Th bjcv fuc b ffb s. Wh hs b s xs f h cuus BSM, c ug, whb h vu f cv b s b 4 Hbch (004) s h h sc cs whch h sk s s h fw w gu cvgc. Thus, h v f -h- fw wu css cvg usg h Ms-Kh sg. Ths sc cs, hwv, s cv b h B-Subh fu.
gs bu h u h k, jcs g f scss h c -ffb. Th j f v sus h u h Nw- Rhs h. Th k ws us f Nw-Rhs s suz b Jck (006) wh ss h Cv ws hs h h bs -u h f chc f h -fg f sh fucs s Nw s gh. As, hs s ws s. (. ). Wh u fcus s Nw-Rhs, w cs h ghs. 3. Nuc Pcs Esg cg wh cu css vvs h us f sc, fg hc x cuus csss. R s hs ssu xc h u, bu cu sfw g s s ub cs, wh gus x v b L L (0). A sc sc f whch uc cs s v s h qu x f h Guss cuuv s fuc. Gv h h Guss s c b g, cu gh s css v hs cc u h cg, h su w b cc s g f c ccuc. Th sv w-kw xs, f h scb h cssc Abwz Sgu (97,. 93-933), s scuss bks s (. g., Chss (997,. 88-89), W (998,. 0), Hug (998,. 87-88), Wh (006,. 5)). Ax B w shw h fu ccu s h bb c s vs h v css sks. W susc h s cu gs s h bb suffc g hs b v. W x u w gh gh f hs cc f s susc h ccuc h bb s suc f cu u sus. Ths b h cs h s cs whch uss uw f hs cu ssus. 4. Cu Mhs A ccus sus f hs su cuc usg h ssc cug g R s cbu ckg, Rf (Mch (0)). Th ccus us s quu cs hc (8-b sg). Ths ckg ws fu c v h cs f h c s f ubs. 5 g, h hg s fu-s css. Fs, w k ssus bu h uc vus f h us hs us h BSM fu b h 5 Th R c s vb f h uhs u qus.
c f b v f cs. Th sfw ccs h s us h, s w s h ub f bs qus f uc sg, ucs h s vu vg. Ths uus cb wh ss f h fuc GBSO h cbu R ckg fos (Wuz. (03)). Sc, w v h xcs cs css w g f ss h ccus f BSM cs. Ths cs h k s h ssu k cs f s h s ug wh kw v, quv xs, vus sks. Th, w vs h css b ssug h h BSM cs h k cs us hs cs s h vs usg f h vus hs bv cjuc wh scf qu u c. Bcus h k cs fc h BSM ss, h sug vs shu b h s css sk cs. Fuh, w g gh f h vs css h g f sks cvg fu xs. W cs sv fcs cu ssus h fuc h sh f h v s. Fs, w v h uc cs f h gh. As scuss vus, h uc cu ccu v s wh h s s c h s wh s c f h k c. Bcus hs vsg c us fc BSM cs hgh g f cs, h c c b s f bw sg. W x cs f 0.0, 00, ch s f - 5. 6 W s x sc fc u cs, h u f h Nw- Rhs h h v f h h chqus. Wh vus sch hs f hs, c su sgfc chgs h gh s uu. Th bs css us h s f Ms Kh (98) gv qu (7). Oh chqus qu v. W s wh - s h w f h v h Ms-Kh sg s h u f h v. 7 W s x h qu u. Ms sus f h v s hv b xchg-s qu s. P h 000, xchg-s qu s us f sxhs f s ss h $3, us f ghhs f s $3 6 Tc s gu cvgc, fc, s w vus scuss, h su c vg sgfc f h su. W cs h gh hv f f succssv s c v w sv gv f. W s s xu f,000 s, whch h gh ss h v s cs b h f s, v hugh h s gh b wh h scf c. 7 f cu sus v f z, h vus f s sv gv f, sug bbs f z, g ss. N h sg v wh bw z s b. f h v s w, s sws w h css. W b fw fus cvg wh gv. 3
. Au h 000, qu s bg g us f $0.05 f s ss h $3 $ f s $3. Sg 007, h CBOE w s g whch c s s. Ov, s hv b h g. Rc h h cu s h w ccu h BSM c h f h c bck h bck u h v. W ccu h c h u sxhs s. 8 W s f u cs bck h. Ths cs ffcv quu cs, s h c 3 c cs. 9 W w f hs -u cs s cuus, hugh sc skg h cuus u hc ss. 0 W cgz h c ug f g s x f h fc k ssus. W vw h f fc k s chcz f h cs f cuus, csss g wh xs, cs v sk-f. F, w s us h fv f chs svg - qus x hw h f h cs f v. Ths hs h Nw- Rhs, bsc, Dkk-B, sc, Rgu Fs. W vs h cg css g h v wh h cu cs h. Th sug v shu b h us c h s h fs c. Th s cc f hs x us s h w c u s u h fc k cs f h BSM w wh kw v h vsg h css v bck h v h ws us c h s. uv, wu s h su w wu v bck h g v. Bu fc, f w. Ax C vs s-b-s x shwg hw g u v f 0% cs u s v f 8%, vs f sgh h 40%, usg h Nw-Rhs h s v fuh ff wh s h hs. 5. Rsus 8 sg, wh cg s g g s v ucg b-sk ss, w w shw h cg, wh h fcs, c s v ss. 9 Ou hss s vs f cs xchg-s ks, whch scf h s g u. Cusz v-h-cu (OTC) ccs c us g u h s g. Du h g szs, OTC scs ss c u c cs, such s fu sx bu v h-w 0 fw css, c ug c ush h c bw s w bu. F x, 30- suck $8.50 hs BSM c f $7.77 wh w bu f $7.7708. Th BSM c wu b u $7.77, whch s bw h w bu. cu k, s c wu k b h w bu u u, hs cs, $7.78. Th vs 5.% (BSM -u c), 4.94% (c u bw w bu), 7.03% (c s w bu u u css ). Ths ffcs suffc g b f cc. Of h 84 cbs f xs sks x, hs w bu v ccus fv h css. css h vs ffc. 4
Th s c s s $00, wh h sk c s v f $75 $5 cs f $5. Th s s 4%, h s x 7 s, 30 s, 90 s, 8 s, csg s x f 0.09, 0.08, 0.466, 0.4986, scv. Th v s s 0%. Rc h w g h cs bs hs s. 5. Ss U us Cs Ou fcus s h Nw-Rhs h, s s k b h s w us. Th sg vu f h Nw-Rhs h s h fu f Ms Kh (98), qu (7). W s cuc ss usg 00% s h sg, gv h v wu b bv 00% f qus. Ths sus ws fus cvg. Fgu shws h vs b sks usg h Nw-Rhs h u h vus ssus css bv. W s h wh c f 0.0, h qu hs shw s cu, h f v s. Th s s s uc f h shs us s vu -xs f h gs u, whch s css wh bsvs f sus usg k. Mv, v hugh h xcs cs sc u h -h- cs, h vs uch hgh f h u-f-h- s h h csg -h- s, whch s css wh c bsvs bs k cs. Wh h css cs f s 6hs, csg h c 00 ch s ucs sg c ghs. Y fc hs ghs s h chcscs f sks skws h f bsv wh k. Wh cuus cs, w c shws v, xc f ch s c whch cs h s ss. Bu f cus, s cc, scs c ccu cuus cs, ch s c s v uk b us s ghs. Thus, w s h h Nw-Rhs h s g u h sg v h ws us c h s css sks. fs u h v h ws us h fs c, h vs us shw f s., f h Nw-Rhs h w hv cuc ss bs h sg s f Bh, C M, L. W cu f ss h s sus. Usg u xs vs ugh x f h ffc f h sucu f v, hc, cb wh h s ffc, w cu x h v sufc. Ou fcus, hwv, s h c f ff xcs cs, s w w f csuc v sufcs, whch qu s g f shg g ub f xs. 5
As, w x fu h chqus f svg f h v. Ths g chqus qu sg v. F hs s f ss, w us - h Ms-Kh sg s h v. Th sus shw Fgus 3, 4, 5, 6. Th sus f h sc h Fgu 3 vu sgushb f hs f Nw-Rhs. Th bchk su f v f 0.0 css sks ccus wh cs qu cuus wh ch s c v h scc ccus f h ws sk. Th gu fs h, Fgu 4, ucs ss s skws sks f cs qu sxhs f gs f c, w c vs vu v. Sxhs cs uc skws sks f cs. P cs uc s f c f 0.0, bu h s us skws sks f w c. Cuus cs uc f css s gss f c. Th bsc h, us Fgu 5, ss skws sks, w c ss xcb h b. Cuus cs v b v uc h usu su f s vs bg w bw h u v. Fgu 6 shws h h Dkk-B h ucs skws sks f cs sxhs wh v wh w c. F cs s, ss ccu f c f 00, wh skws sks ccu f ch s c. Cuus cs g ss f c f 0.0 00, bu u cs v f ch s c. Ths sus s s Nw-Rhs h sc h. O gh sb sk f h v ss h s f hs ss bsv c, whch s s v -h-. Af g v f s, w f h s v s b ss h s u 5% b h usg Nw-Rhs wh v sh- s. Ess bu % f 0% kw v, f 0%. 5. Bsc Dscuss Ass f Nuc Rsus T c, w f v ss f g v h v f s c ccg h BSM. W x h s ssus s h b ug s sxhs. W f h h Nw-Rhs, h bsc h, Dkk-B uc v s vsu sus, bu h fg s h cfg. F cs qu 6hs s, h sc v ss, wh h hghs vs ccug wh h w sks. 6
O suc f cu cu b h sg. s w kw h chcs c sw w h s css h uc. Wh s ssb chcs, hwv, s ffcu ssss h c. Mv, h c x w cuc, w qu kw h su. Hc, u chc f h su cu bs u sg s. W csqu subjc v f h Hsbg Uc Pc: c su shg whu g. Thus, h sg cu w b v g b h w c ssss hs. Tc c hs ffc s w. Hg vhg s cs, s c c s f h s, bu c f. P c, whch w susc s c us sch cc, s bb s ugh. W sus ub h uss qu c f ch s, bu h bb shu. C h fc s c ug. Cs c c u g f cs hgh h h qu u. B fcg u c, c gv u c c v f -u cs. F x, sus cs qu s, sf, h hc ucs cs u h c cs. A c f $0.5 c v f -u (hc) cs f $0.45 $0.54. A c u u w hgh v, wh c u w w w v. Ths x c x f h s, hwv, sc wu h h vs wu b uf hgh w. Th vc shw h suggss h bs hgh vs uch c h bs w vs. Mv, h ffc sus f cuus cs u cs s cu g. S c ug c x f h ffc. 5.3 Fuh Ass: Th g Effc W x u ss s fuh b xg ssb suc f h b. f h suc c b f, cu c hw ss hs ssu wh s wkg wh cu cs h u v s kw. W fcus h sus f h Nw-Rhs h, such s s w us gvs v s sus sv h hs. Th vg f s h vv f h c wh sc h v. svg f h v usg Nw-Rhs, h v qu cvg s b h vg h sc f h fuc f z. Thus, h vg 7
v cu s wh h b s. Fgu 7 w shw sgh gu uc f h fs gh Fgu C, h cs f c ug c f $0.0. Th sks Fgu 7 sc cs ($.50 ) bu cv h s g, $75 $5. P A shws h s sf, wh P B shws h vgs css h csg gs f ss. K h s su f hs bg x, w kw h u vgs bcus w kw h u v. cc, kwg h vgs wu b b, s w ss. Phs susg, h vgs x w f h s gs f ss whch h vs qu hgh. Lw vgs suggs h wh g, g v chgs qu v c b s u. A csu x f h vgs shws h wh h bw 0.5, h vs v subs f h u vs. Thus, w hv sub usfu u f hub. O gh sb gu h wh vg < 0.5, h s v suffc cfc us h v. W gh s h h c v b fv (NR). A h s NR shu bb b sc. Th s c b fv (R). Nhss, h w -v bs wh such cuff. hs x h u v s kw, s w c s h u vgs. cc, h u v wu b kw, s w c h u vgs. Px vgs cu, hwv, b b f h vs f h hv b v. Fgu 8 shws h ffc bw h u vgs h x vgs f f h xs. Wh h xc f h -h- cs bg z, ffcs gv, g h h x vgs g. s css, such s h hghs ws sks, h csb g. Thus, g x vgs k ss h 0.5 cuff. Thf, w cs h sk h s h NR bs h ukw u v R bs h x vgs. Bu h s chc. Th u vgs wu b kw. Rgss f whch v s us ccu h vgs, h vu f cu f s NR bs s vg qus ccu sg s fws: S : Ccu h v. S : Ccu h vg usg h v. Th vg s us c h Nw-Rhs h, bu h h fu hs. Ths hs, hwv, c sc ss f h sh bw h c h v. Thus, h fuc b h cc cu b h vg. 8
S 3: f h vg s bw h cuff, ccu h h v s b fv (NR). Bu f h v s NR, hw c us cu h vg S? Th vg wu, hf, hv b NR. A f h vg s NR, h hw c ccu h h v s NR? A s. Thus, s g ccu h bcus hs b ccus wh v w vgs, cu us u vg s sg f wh hs b xss. Ths h s v us b OMcs, whch s v f h vg s bw 0.5. 3 W w kw h hs ch s ccu. F h bg, hwv, us g h ccu sg xs h, hs v cc, b. T, h u hs h v s s hugh s cg sccs h hugh s f k fcs c h BSM. Sus w s b c u u cs h c s hs f c scc. F x, us csvv jc v s u f % h c, u ss h h b-sk s. Fgu 9 s Fgu 7, bu h f h cs hv b f b fc f.0. Fgu 9 c ks x s sh Fgu 7, bu h gus f h vs vgs qu ff. F x, h 30- (x = 0.08) 75-sk. Whu h u, s v s 36.87% s vg s 0.36., hus, s NR. Wh % cg u, hwv, s v shs u 58.98% s vg s.47, whch wu k R. Nw, cs h c f hs su. W hv u-f-h- h w kw f hs c x s c v f 0%, wh h c u ff s wu b cc. s v 37% s s wc h u v,, sgg h ccu gc, s vg s s w h shu jc s bg NR. Bu f h w c s % u v BSM, s wu b f h fcs h c h s, s v s w s h s h u kw v s vg s suffc hgh h s R. s qu xg bv h fcs cu k c v b. A wh gh sb ssu h h s c u ccu f k fcs, c u cu s ccu u s us cg. Thus, w f ccu h c s v c b NR wh s fc k 3 s c hw OMcs jusfs g v wh vg s ss h 0.5, wh hs hv v s h vg. 9
s vu cs ccg, bu bcs NR fc k wh b cg ffcc. Mv, f b vg cuff w usfu u f hub, shu h u u ccu cus. Ufu, s. Ag h u f hub wh c f 00 sus h jc f uus css f s whch h v qus h kw v. F x, wh 90- s, w wu jc sks f 77.50 75, v hugh h vs 0.0. F 30- s, w wu jc sks f 85 bw v hugh h vs s cs 0.0. F 7- s, w wu jc s wh sks 90 bw v hugh sv f hs s hv vs f 0.0. Mv, sg b u cus cs h vs vgs s h h bc R, wh h w NR h bsc f b cg u. 4 A bvus qus s whh h s v h wu wk b. ss uk h s wh s, such s ju-ffus schsc v s, cu ssb b f f hs b. Phs ss-scv wu b b. s ssb h h -f v, whch svs f h v f h bbs whu ssg hugh f, cu b b v. Ufu, Jg T (005) f s cu ccs h s w. Mv, -bs -f vs bh qu h xsc f qu k b g f sks, whch c b b f vu qu s. 5.4 Ec Ess f h c T hs w hv shw hw u hhc s ssu b c fc k b h BSM wh kw v uc v s hugh h b f cu hs u h g v. wu b vub xcs s f w c s hw uch f h ss bsv cc ccu f b hs cu b. Th b, hwv, s h u hs w hv us hhc s wh kw v. Wh w u h w f s g, hwv, w u h b h h u v s kw. Sus w us h v f h h s css -h- s x f h kw v. A-h- s c h s w, s h 4 W s cs fuh ssb f uzg h b. s f ccug h v, gh b b ccu h vc. Ufu, h vc vg s s ws f - u-f-h-. qus h vg v b w s h v. Thus, f hgh v scks, h vc vg wu b v w. 0
f s kg hs s. Th vs shu s ccu fc h k cssus, v hugh h css s h u v. Rc h w us h c s f s f B s. Fgu 0 shws h vs bs h k cs f h B c s us cs h vs bs c f h B s. As, w us h v f h x -h- s h kw v. Th k vs hgh f h w sks, bu h shs kb s, cu h s whch h cuv ss ug uw bh bv bw h sk. W w hv w ss f v ss, s w c s h f h c s ccu f b cu ffcs. Sus h w f h gu f h s s h su f h squ vs f h vs f h kw v bs k cs. Th w f h gu f h s h ss f hs cu ffc s h su f h squ vs f h cu vs f h kw v bs cs. W h xss h f h h f b: N N c,, ( ) ( ) F hs B s, us u b x 40%. Thus, f hs qus, w s h h cu ffc ccus f bu 40% f h bsv s. W w uk f xsv c ss. D cc f h OsMcs s qu bss (Ju, A, Ju, Ocb) f 004 00 f s h cu h scks h Dw us Avg s w s h S&P 500 Nsq xs, g f 896 ug-qu cbs. A f hs s hv x h g x. T hs, w hv ss Ac-s,.., xcs, ssus hw h gh ffc hs cu ccs. Nhss, s ssb v c sus whu ccug f h xcs fu Ac-s s, whch h f s vu scks. Thus, w cu h vus usg h b, whch cs h ffc f xcs h s v b vs. Of cus, h S&P 500 Nsq x s Eu-s. A cs bs h f h b-sk s.
T w f cb css h ug scks s w s v s cs u g f - u-f-h- s, h sk cs uc h cs css 0% bv bw h cus c f h ug sck. s css, s g w ugh ch h 0%, hs css h sck ws f h ss f h qu. Ths ss ccu jus 0 f h 896 css. W hv s bv h u s f s w bu. Rc h u hhc s, h gs cu ffc ccus w w f h -h- xcs c. Bu wh wkg wh c, f hs s suffc uc b cs, w c us h. Tucg u sks 0% bv bw w su ss f s bsvs f whch h cu ffc s k b h gs. Thus, u ss c w bus. Ag, w ssu h h v f h css -h- ss h u v. Ths v s ccu hugh h NR gh wh c f h MK s. A f h s h c usg b wh,000 ss. Ac xcs s k ccu, LBOR s us s h s. Ths cu vs -bs c f ch f h s. Th - f h csg b-sk s s us s h k c f h. Th v s h ccu f bh h k cs, g usg h NR gh wh c h MK s. Ths sus us ccu h -ssc v s f hw uch f h c v s s u cu ssus. Tb ss h, s v, xu -cs f ch ug. Th vg s 7.96% wh xu vus s ug v 80%. 6. Ccuss hs, w x sg sufuus qus. Sg k fcs s, c us kw v c h vs-g h g v f h c? Th sw wu bvus: c su cv h g v. As w shw h, hwv, cvg h g v s s sghfw. fc, cv vs s s css sks h kb s ss, sks, skws. Mv, hs s s uc f sh- s, s s h cs f h ss bsv sch cc. W shw h wh h chc f -fg chqu, c, sg v,
h h f c ug c uc hs s, sg x s h hs. s g gu h hs ffc s ch, c buc f cu css bu hvg gfu sgfcc. Y vw f h u shws kb bsc f cu scfcs, h ffc s hv b b schs. Suggss h cu s sc bsvs h uuswh u xcssv w vgs g h fc h us ccu gc: h v s qu h vg, whu wu h us h vg f h v c b us. Mv, s w shw, wh h fcs fuc h s, s wh uuswh cs w b, hb bg hs bs f h h fcs h v. A v f hs ccs w h, h s vc h u h hs v sc bsvs f hs s. A cs jc bsvs s such sch sg h su wu hv b. C h b b fx? W c css g hs s b cg h cs u quu cs g ch s c. Y, g h f qu wu qu g cs wh 3 cs. k h xchg-s s us v 30 s v f sxhs s, v wh cg, w c s bsv v ss wh s c b Bck-Schs- M. A su, g 3 c cs wu xc h x hgh css. W k c h h ffc shw h s h suc f h s. Ou c ss suggs h w bu s u 8%, bu w f csb vc h s hs ffc c b x hgh, s shw Tb. Ev u h s csvv s ssb, f x -ffh f su s v b css b h sch h s bvus fx, h csb gus f cc bh sch g. W f wh h sccg ccus h h v ss bsv cc cu b sgfc bs, whch c fs cg sgs, g sgs, bg hg scs h shu b sk-f bu fc c subg w z f uc. 3
Ax A. Pf f Th Usg h sc- T h f F(x), w hv wh s bw x x w hv f v = 0,,, F ( ) F x F x F x x x x x! ( ) ( ) ( )( ) ( ), x. Usg h Nw-Rhs fu (6), x F ( ) ( x ) F ( x ) Sus h. f w chs h x, h w hv f 0 f sc F(x 0 ) > 0 F (x 0 ) > 0. W s hv Fx ( ) x x x, x 0 0 0 F ( x ) 0 F ( x ) F ( ) ( x ) 0, sc ssfs F"( f ) > 0. Thf, x x. Sus hs hs 0 f f, w v h + cs. Wh x f Fx ( ) x x x, F ( x ) x F ( ) F ( x ), w hv ( x ) 0, f wh s bw x f. Thf, x x hs f. Th Nw- Rhs h s cvg sc h squc s sc csg bu bw. Th v s h uqu su f h f F, s h gh us cvg. Th s x x F ( ) F ( x ) x ( ( )) ( ) ( ) ( ( x )) ( ( ) ( x ))/ x ( ) ( ), wh h sc fws f h vg v fus. F h csg f h fucs ( ) ( ), w b h qus, Ax -
x ( ( ) ( x ))/ ( ( x ) ( ))/ x, ( ) ( ) ( ) ( ) S f h cs < < 0 wh ( ) 0, h gh s cvg f f ( ( x ) ( ))/ ( ) ( ) f. Th f f h sc cs () s h s, wh s sv csg s csg gv. Ax B. Es Effcs f h N Pbb hs x, w s h h s f h bb c x f x s h c g -f cuv f h v gs h sk. L c M b h bsvb kw cu k c f Eu c. Ths vu s h k s u ccu h v h BSM cg. Th v,, s f f h fwg qu: c SN ( S,, K,, ) K N ( S,, K,, ), M S K ( S,, K,, ) ( S,, K,, ) ( S,, K,, ) (B.) whch h ukw s fuc f h sk c K f h us f hs. Th sk-f s s ssu b kw, h ug ss c S s bsv h s. Hc, h h s S, τ, s css hughu hs. Th qu (B.) c b sv f h v. Th vu f c s sc csg wh sc v, whch s s h h vg s c c csg, 0. Ths c gus h f su xss, w b uqu. f s c bg-f k, h h fwg bus kw f h vu f h c : (S K - ) + c M < S. Ccv, hs cs gu h xsc f uqu, gv vu f v, s h b s w f. Ax -
Th s fuc x h Guss cuuv sbu s gv b x k k z / ( ) x N( x) z. k k 0 k! (k ) (B.) Th ss (B.) s bsu cvg vwh. Thus, h qu (B.) c b w s f h w ss: k S K ( ) k k c S ( S,, K,, ) K ( S,, K,, ). (A.3) M k k 0 k! (k ) Th uc h sv h v s uc h w ss sv h v b h Nw-Rhs h f fg, s Ms Kh (98). Th h s us bw b vg h uc f h ss. B.. Th v f k = 0 0 Cs k = 0 h w ss (A.3) f h x f h v. Th fwg hs s x f h k c f h Eu c f h x f h v (B.), S K c M S( S,, K,, 0) K ( S,, K,, 0) ( ) 0 0 K K K K K 0 0 0 0 ( ) 0. K K K Tkg h vv wh sc K bh ss f qu (B.4), w b 5 0 0 K 0 K S K wh 0 0 0 0 ( S K ) S,, K,, S,, K,, S 0 K 0 (B.4) (B.5) 0 Ex f h xss f (B.5) shws h b z, s c uc K -cs vs css sks. 5 Uk C M (996), w sv h v c s fuc f h sk c, sc u us us h v s. Hc, w s usg h sg bhv f h s f h v (.., h fc h h s hs u sk c h cs h uw cuv f h v s). Ax - 3
B.. Th v f k = Cs h w ss (A.3) f h sc x f h v. Th fwg hs s h sc (cubc) x f h k c f h Eu c f h cubc x f h v. S K c S ( S,, K,, ) K ( S,, K,, ) M 3 3 S ( S,, K,, ) K ( S,, K,, ) 6 (B.6) S h vus cs, w k h vv wh sc K bh ss f qu (B.6) b 3 ( S K ) S K 6 K K K wh S,, K,, S,, K,, S K S K S K. (B.7) Th xss f (B.7) vs h h sc (cubc) x f K h s Guss cuuv sbu fuc s cus s ffc h cu v, bcus h u (B.7) c chg sg f sv gv. Cs h u f (B.7), fu s fws: 3 S K S K K 6 K F hs, w hv h xc qu f h sk c K h s css ch h u f h v. Th s, K fwg qu: K 0 whch K s su f h 3 S K S K K 6 K.. (B.8) Ex f hs xss shws h h uc x f h Guss cuuv sbu fuc c uc -cs vs css sks. B.3. Th v f k = Ax - 4
Th w ss (A.3) f h -h x f h v. Th fwg hs s h -h (( + )-) x f h k c f h Eu c f h ( + )- x f h v (A.3): S K ( ) cm S S K K S K! ( ) k k k (,,,, ) (,,,, ) (B.9) k k0 k k B kg h vv wh sc K, w b ( ) ( )! ( )! k k k k k S K k k k 0 k k k 0 k K K wh S,, K,, Ax - 5 S,, K,,. Cbg K wh sfcs, w g K k ( ) k k S K k k 0 k! K (B.0) k k ( ) k ( ) k k S K. k k k0k! (k ) K k 0 k! us h s ffc, w us wh h s K * such h h K * s su f h fwg qu: * * k k ( ) * * * k ( ) k k * * S * * K 0 k k k 0 k! (k ) K * k 0 k! (B.) Ths s s u h v f h f x,. N h s, h f-h s f h bv qu chs * * k k ( ) * * * k ( ) k k S K * * * k * * k * * k 0k k K k 0k! ( )! N( ) 0. Thf, h xss cc v 0 such h wh > 0, qu (B.) hs su f K *. Hc, h b ss wh h x bcs csg ccu. Th hc sus suz h fwg h. Th B. L h v b f s h qu (B.), c SN ( S,, K,, ) K N ( S,, K,, ), M S K
Wh Nx () k 0 k ( ) x k k k! (k ). Th -h uc x f h v (B.) f h k c f h Eu c s gv b qu (B.9), k S K ( ) k k c (,,,, ) (,,,, M S S K ), k K S K k 0 k! (k ) S,, K,, S,, K,,. Th h fwg h ss h: S K () Th f chg f h -h v v wh sc h sk K s gv b h fu (B.0) () Th s cc v 0 f h ccuc f h x such h f v 0 = 0, s ffc ccus. Th s s, qu(b.7)). K 0 (h s su f (3) Th ssb sus f < 0 such h h s -h v x f h v hs s ffc. Th s s, K sk K *. 0 f s Ths h xs hw cu xs f h cuuv s c uc s ffc vs. A u, h c -cs vs css sks s css hs vs c u w h uw, h f s. Av, h c k skws sks. Th s h h s f h v wh sc sk b z u h ccuc f h x f h sbu. W hv s v hs shs wh vs h ug, bu h sus cb. Ax C. Ex f h Su f Nw-Rhs Cs 30- c suck 80 whch h ug s 00, h u v s 0%, h sk-f s 4%. Th cu w fw s c h usg h BSM fu. W h s h BSM c bck h fu usg v sch h, w v bck h 0% v. F hs us w us h Nw-Rhs h s g wh h ffc bw h BSM c b usg 0% h c uc b h s ss h 0.0. W us h Ax - 6
ss bw shw h sus usg c cs, hugh xc wh, w fu cs. S : Ob h BSM c usg v f 0%: Rsu: c = 0.667603558 F h us w u hs h s, 0.6. W w s shw h sus wh hs vu u. S : D h sg f h Nw-Rhs h usg h Ms- Kh fu Ms T S K Kh 00 0.04(0.089) 0.089 80.34730943788 T Th Ms-Kh sg gus cvgc. H h sg s 34.730943788%. W cs f hs vu b ug. S 3: u h c f h h s wh h bsu vu f h c f 0.0. Th sus us h b bw. Th ubs bw u f s uss bu u h cus. Nw-Rhs, h c s b s h ffc v b h vv. Guss Pc Dffc Dvv c #.34730943788 35.0835340446-4.8353404464 9.98344037 -.65895 0.704949.548403548 -.88403548 5.5845408349-0.9590 3 0.4948340859 0.55588393-0.9588397.85679594479-388653 4 0.38859687884 0.339883967690-0.0798839676898.960577794-0.068007 5 0.3679658837 0.849399960-0.04939996008 0.5499366075-0.0439946 6 0.880997509 0.68705577-87055769 0.065903306-0.039800 As shw, h css cvgs sx s. Th su s 8.8%, whch s bu 4% hgh h h v us c h. H h g c b u, h su wu ff sgh 8.96%. Ax - 7
Ahugh shw h, h sus fuh ff 4.67% f h bsc h 34.7% f Dkk-B. Th gu fs sc hs cvg. Wh c ug, h sus 9.33% f h bsc h 4% f h Dkk-B h. Th s cvgc f h gu fs sc hs. Ax - 8
Fgu. S, B C Os, Ju 8, 03, xg Fbu 6, 03. Th sck c s $54. h sk-f s 0.05%. Th cs k f h CBOE s wb s h cs f busss. 0.80 0.70 0.0 35 40 45 50 5.5 55 57.5 60 6.5 Sk
Fgu. Ss, Nw-Rhs Mh A. O Pcs Sxhs 6hs cs, c = 0.0 6hs cs, c = 00 6hs cs, c = ME 0.90 0.80 0.70 0.0 0.35 0.5 0.0 0.5 0.05 0.5 0.0 0.5 0.05 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s B. O Pcs Ps cs, c =0.0 cs, c = 00 cs, c = ME 0.90 0.45 0.45 0.80 0.70 0.0 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 0.35 0.5 0.0 0.5 0.05 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 0.35 0.5 0.0 0.5 0.05 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s C. Cuus O Pcs
cuus cs, c = 0.0 cuus cs, c = 00 cuus cs, c = ME 0.80 0.70 0.0 0.45 0.35 0.5 0.0 0.5 0.05 0.5 0.0 0.5 0.05 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s
Fgu 3. Ss, Sc Mh A. O Pcs Sxhs 6hs cs, c = 0.0 6hs cs, c = 00 6hs cs, c = ME 0.90 0.80 0.70 0.0 0.35 0.5 0.0 0.5 0.05 0.5 0.0 0.5 0.05 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s B. O Pcs Ps cs, c = 0.0 cs, c = 00 cs, c = ME 0.80 0.45 0.45 0.70 0.0 0.35 0.5 0.0 0.5 0.05 0.35 0.5 0.0 0.5 0.05 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s
C. Cuus O Pcs cuus cs, c = 0.0 cuus cs, c = 00 cuus cs, c ME 0.80 0.70 0.0 0.45 0.35 0.5 0.0 0.5 0.05 0.5 0.0 0.5 0.05 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s
Fgu 4. Ss, Rgu Fs Mh A. O Pcs Sxhs 6h cs, c = 0.0 6hs cs, c = 00 6hs cs, c = ME 0.90 0.80 0.80 0.70 0.0 0.70 0.0 0.0 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s B. O Pcs Ps cs, c = 0.0 cs, c = 00 cs, c = ME 0.90 0.80 0.80 0.70 0.0 0.70 0.0 0.0 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s
C. Cuus O Pcs cuus cs, c = 0.0 cuus cs, c = 00 cuus cs, c = ME 0.90 0.70 0.70 0.80 0.70 0.0 0.0 0.0 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s
Fgu 5. Ss, Bsc Mh A. O Pcs Sxhs 6h cs, c = 0.0 6hs cs, c = 00 6hs cs, c = ME 0.70 0.80 0.0 0.70 0.0 0.5 0.0 0.5 0.05 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s B. O Pcs Ps cs, c = 0.0 cs, c = 00 cs, c = ME 0.70 0.80 0.45 0.0 0.70 0.0 0.35 0.5 0.0 0.5 0.05 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s
C. Cuus O Pcs cuus cs, c = 0.0 cuus cs, c = 00 cuus cs, c = ME 0.70 0.5 0.5 0.0 0.0 0.5 0.05 0.0 0.5 0.05 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s
Fgu 6. Ss, Dkk-B Mh A. O Pcs Sxhs 6hs cs, c = 0.0 6hs cs, c = 00 6hs css, c = ME 0.90 0.80 0.80 0.70 0.0 0.70 0.0 0.5 0.0 0.5 0.05 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s B. O Pcs Ps cs, c = 0.0 cs, c = 00 cs, c = ME 0.80 0.80 0.45 0.70 0.0 0.70 0.0 0.35 0.5 0.0 0.5 0.05 75 80 85 90 95 00 05 0 5 0 5 75 80 85 90 95 00 05 0 5 0 5 75 80 85 90 95 00 05 0 5 0 5 Sk Sk Sk 7 s 30 s 90 s 8 s 7 s 30 s 90 s 8 s 7 s 30 s 90 s 8 s
C. Cuus O Pcs cuus cs, c = 0.0 cuus cs, c = 00 cuus cs, c = ME 0.80 0.70 0.0 0.45 0.35 0.5 0.0 0.5 0.05 0.5 0.0 0.5 0.05 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s 75 80 85 90 95 00 05 0 5 0 5 Sk 7 s 30 s 90 s 8 s
Fgu 7. s f Cs Sck c = $00, sk gs f $75 - $5 $.50 vs, sk-f = 4%, u v = 0%, xs f 80 s (0.4986), 90 s (0.466), 30 s (0.08), 7 s (0.09) s shw; su s b usg Nw-Rhs wh c f $0.0. O cs u. A. s B. gs
Fgu 8. Dffc bw Tu gs Px gs Px vgs b b svg f h vs usg h cu vs b h vgs.
Fgu 9. s f Cs wh % Pc Pu Sck c = $00, sk gs f $75 - $5 $.50 vs, sk-f = 4%, u v = 0%, xs f 80 s (0.4986), 90 s (0.466), 30 s (0.08), 7 s (0.09) s shw; su s b usg Nw-Rhs wh c f $0.0. O cs ccu usg h Bck-Schs-M f b % u. A. s B. gs
Fgu 0. S, Mk M Pcs, f B C Os, Ju 8, 03, xg Fbu 6, 03. Th sck c s $54. h sk-f s 0.05%. Th k cs k f h CBOE s wb s h cs f busss. 0.80 0.70 0.0 35 40 45 50 5.5 55 57.5 60 6.5 Sk Mk cs M cs
Tb. Ms, S Dvs, Mxu us f h Rv P f h S Accu f b Cu E Ess f h ssc f h Dw Js 30 scks h S&P 500 Nsq v 004-00. D k qu vs wh x h u. Th v f h -h- s us s h u v. (b cus x g) Sck M S Dv Mxu AA 8.99 4.08 87.69 AXP.4 3.7 40.49 BA 8.35 3.3 6.57 BAC 7.00 9. 94.9 CAT 7.98 5.77 74.04 CSCO 9.76 5.74 78.45 CX 8.55 0.04 75.4 DD 7.68 6.87 44.6 DS 5.09 3.5 77.6 GE 30.76 5. 77.6 HD 4.53 3.49 8.7 HPQ.99 0. 85.56 BM 7.3 8.95 79.97 NTC 7..9 9.98 JNJ 7.9 9.38 63.94 JPM 9.6 4.0 88.85 KO 4.47 7.84 50.8 MCD 7.67 6.8 64.5 MMM 6. 6.6 5 MRK 3.78 9.67 90.74 MSFT 8.6 6.4 89.6 NDX 6.38 8.67 4.90 PFE 30.9 4.4 83.39 PG 5.84 4.56 53.44 SPX 4.98 6.7 47.5 T 8.9 0.86 95.7 TR 5.30 9.50 33.66 UNH 0.5 6. 67. UTX 4. 3.83 59.8
Z 8.65 5.65 96.34 WMT 5.53.98 90.56 XOM 0.3 4. 6.00
Rfcs Abwz, M.,. A. Sgu (97). Hbk f Mhc Fucs wh Fus, Ghs, Mhc Tbs. Wshg, DC: N Buu f Ss. Bksh, G., C. C, Z. Ch (997). Ec fc f v cg s. Th Ju f Fc 5, 003-049. B, W., A. Ss, D. Ss (006). N cx cs sss. Ju f N Scc Nuc Su 7, 9-96. Bs, D. (99). Th csh f 87: Ws xc? Th vc f s ks. Th Ju f Fc, 46, 009 044. Bh, M., Chsfs, N., Sk, G. (996). Cug h Bck-Schs-M v. Avcs Fuus Os Rsch, 8, 5 9. Bck, F., Schs, M. (973). Th cg f s c bs. Ju f Pc Ec, 8, 637 653. B, N., Wh, R. (004). Ds bug ssu ffc h sh f v fucs? Th Ju f Fc, 59, 7 753. B, M., Subh, M. (988). A s fu cu h s v. Fc Ass Ju, 5, 80 83. Bw, S. (990). Esg v. Fgwsk, S., Sb, W., Subh, M. (Es.), Fc Os: F Th Pcc. Hw, L: Busss O w. C, L., Fgwsk, S. (993). Th f c f v. Th Rvw f Fc Sus, 6, 659 68. Chb, J.-L. (.) (999). Mhs f Fs Ps. Ch. 3 A Hs f Aghs: F h Pbb h Mcch. Nw Yk: Sg-g. Chbs, D., Nwkh, S. (00). A v ch cug v. Th Fc Rvw, 38, 89 00. Chc, D. (996). A gz s fu cu h v. Fc Rvw, 4, 859 867. Chss, N. (997). Bck-Schs B: O Pcg Ms. Chcg: w Pfss Pubshg. C, C., M, T. (996). A s ccu fu cu v vs. Ju f Bkg Fc, 0, 595 603. C, C., Su, T. (996). Skwss kuss S&P 500 x us b cs. Th Ju f Fc Rsch, 9, 75 9. Ds, S., Su, R. (999). Of ss sks: A sucu scv. Ju f Fc Quv Ass, 34, 39. Ds, P., Mhw, S. (009). Mcsucu bss c ss f cg s. Rvw f Dvvs Rsch,, 69 9. Dus, B., Fg, J., Wh, R. (998). v fucs: Ec ss. Th Ju f Fc, 53, 059 06.
Fg, M (0). O g BSM v. Wkg, Uvs f S. G. Avb h://www..us.u.sg/csf/wbgs/uhs/ff/f/fg%80040%9.f Gh, S. (0). C Th b Exc Fu f? Wkg h://s.ss.c/s3/s.cf?bsc_=7994. Hbch, W. (004). A v Es f Bck-Schs-M, wkg vb h://s.ss.c/s3/s.cf?bsc_=5677. Hug, E. (998). Th C Gu O Pcg Fus. Nw Yk: McGw-H. Hsch, L. (003). Es v s. Ju f Fc Quv Ass, 38, 779 80. Hs, S. (993). A Cs-F Su f Os wh Schsc wh Acs B Cuc Os. Th Rvw f Fc Sus 67, 37-343, Hsh, D. (99). Chs N Dcs: Ac Fc Mks. Th Ju f Fc 46, 839-877. Hu, J., Wh, A. (987). Th cg f s sss wh schsc vs. Th Ju f Fc, 4, 8 300. Jck, P. (00). B c. Wkg vb h://www.jck.wbsc.vg.c/bc.f Jg, G. J. Y. T (005). Th -f v s f c. Th Rvw f Fc Sus 8, 305-34. K, M. (006). Fs vs v h c fuc h. Th Fc Rvw 4 (589-597). Kz, M. (99). Wh cs kw bu sg v,. Fc Ass Ju, 47, Ju-Augus, 5. Lé, H., R, R. (976). S vs f sck c s cs. Th Ju f Fc, 3, 369 38. L, S. (005). A w fu f cug v. A Mhcs Cu, 70, 6 65. L, M., L, K. (0). A v succssv v-x h f cug h Bck-Schs-M v. Quv Fc,, 45 69. Mch, M. (0). Pckg Rf: Mu cs fg- b., Aus: R Fu f Ssc Cug. Ms, S., Kh, G. (98). Th ccu f vcs f h Bck- Schs-M : A. Th Ju f Fc, 37, 7 30. Mhw, S. (995). v. Fc Ass Ju, 5, Ju-Augus, 8 0. M, R. (976). O cg wh ug sck us scuus. Ju f Fc Eccs, 3, 5 44. M, R. (973). Th f cg. Th B Ju f Eccs Mg Scc 4, 4-83. Muhusw, J. T. Hs (0). Dscc bw Bck-Schs b. Wkg, K S Uvs.
P,., Rub, G., S, G. (999). Wh w s? O h s f h v fuc. Ju f Bkg Fc, 3, 5 79. Rubs, M. (985). Nc ss f v cg s usg s qus h 30 s cv CBOE csss f Augus 3, 976, hugh Augus 3, 978. Th Ju f Fc, 40, 455 480. Rubs, M. (994). b s. Th Ju f Fc, 49, 77 88. Schs, R., T, R. (978). C sck v xcs b. Th Ju f Fc, 33, 9 47. Shw, W. (998). Fc Dvvs wh Mhc. Cbg, U.K.: Cbg Uvs Pss. Shu, Y., P, G., L, S., Wu, T. (00). c f bug ssu chgs v: Bf f h s f h sub css. Th Ju f Dvvs, 7, 54 66. g, G. (009). Th Bck-Schs-M s f h v s: A su su. Ju f Ecc Bhv & Ogz, 7, 03-8. Wh, R. E. (006). Dvvs: Mks, u, Rsk Mg. Nw Yk: W. W, P. (998). Dvvs: Th Th Pcc f Fc Egg. Nw Yk: W. Wuz, D., hs. (03). Pckg fos: Bscs f vu., Aus: R Fu f Ssc Cug.