L5 - MSFE 2011 FOUNDATIONS OF FINANCIAL ENGINEERING...

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Unformatted text preview: MSFE 2011 FOUNDATIONS OF FINANCIAL ENGINEERING Instructor : Rama CONT u x ------ ..... ............................ ................... ............................................... ...... chftsenla Han» of make} uncerfainjj Consider a financial market in Which we can trade some "primary instruments" . . . . . n (Stocks bondwdlces) In any ‘1‘”an atpflces , . 5m, ,_ __ , s (t) fix : a: :hme: harem: T70; : i #0. : : ,‘naoi’: :: ..7HTMWWSI‘MCMMZOA 1T ; setofdates,canbe discrete fzyolAhm/Wm T] or continuous '. if = [0,11] The present value of these prices is known but their future values are unknown. Each possibility for the future evolution of market prices will be called a 'market scenario' A market scenario is the specification of the evolution in time . of prices of all primary assets: ' w m am ' 52 Ha 5a a} ' W‘ my; (4)652 denafas a. marital“ SCeflaNo‘ w 7560 ‘nfocmahofliiiii WIT/:P):iiiiii ...”’:::::"' .L’seriofjwipamcevents : Comer. aiooafc tefl , b0. : : : idunnj [0,7]: : 3 3 NW}: St} “3 Wm“ (Sway/0.5”“); 3 :0? Pm ‘izrrvmzoétvék‘ “5 been chime 3 i i i ‘ ‘ ‘ “ 1 Le!” ids: {RC}. Hm Serif emits: @56th +7. ~— ' i5 0» 66M4*417&L)m OCfi—ij: : 5M6!” cf ‘:3 M1 cm: Wu 0013, defend on: He: fasting: be dafe it. fffi‘f @2775} 5'57} 5593; "/fijter’SM’W’Jfi/m’éi’ 3 f f 3 f f } ff 3}}???03Z2339m‘?-Wm iiiiissszziiizzz zziiiiiii :iiv’vvggm: :afdahg {7, 35 ins \cerf‘am7: Hg iii: ' : :CIHW :‘hGfide’ 0F KW ihCPfCHECd/i 3 3 : : : i i i : i, EUMPQMCQH oPh'onj. . . . . . . . . .. A . SEMFM (41’ i i A; 3 Europe“ . . . . . . . , , , 09M w Mew m s , , , , W: W New W , 3 3 3 3 6m,“ , (“dawn”) , K . . , sde {am-saga) K i i i i : 3 3 3 3 3m Hm raw W) n by mm W _<‘opwon'2 r» sell, , 3 3 3 2 (Mb Wk of am 5 ML omwfdf MM 5 ML ,,,..., dafe T fl? Pate K 0W3 T ,4" Price K (Fixcd mm 4? swam/1w) : (W M W 4+ BMW“ 1 I I » WSW) ..:: ~ 1?: {WW 3W a when : z—a 3 Hz-+3(sm—KHZO 333333: .9 {5M 3 (m no!’ “‘6 055mm) 125 L33 sa+ T flunk ; 31;; my; mm a da‘egkezng W; "ac/21 ' Tb ' somebozl] are ' EH.':'_'(5(T)-K)+ $0 ' ' ' ' " —> w ébfiab‘m h 56% SF*T24*WK “M W - u: {WWW {5 “£05 ATM—J7 Lamfl M‘ €04" thbn) _., rin‘ (bf no!" He obti‘ah‘m “3 86% af’ ber{onte/< a m weir 5a? ?< log mm? m i wise/i Ms W aw? ? ? ? ? ? ? ....”F.ZOEP‘3’HQ.“*‘ mamz'fjmiiijfmm 91¢ 2m use; aw Hm Web”??? Fiji M WM M} Z Z E f f 3} "CM/ad :iPw 'Pmm‘um (on «90'in «fl: He 'ogah‘m ' ' ' ' ' ' : : i iiiii acmwo m T‘K‘s‘mf “iiiWiiiiiii Pm - dependent options PayOff can: depend'o‘n the behavior of underlymg asset : not just at a Single date but during Whole lifetime Of option ‘ AM we W m W min-kg K fixmdafasl' e m ASWX jaw afgh‘on ; 2 (K‘ ‘1' Z 897)) n a“! + 5x2; :Barrr’cf :Oths ; veg «mm m: fixajn’-wwpe kelp}:pr . , , , . . . , W W , .chkéwjfi'} 3M, , W“ WM W: K, «W B , , , , 3 3 3 : 2sz 3 it Kesm 1? Wm 33w >3 “MEEONWW_,_333E§_M_ H :Z ,(:K-.-S(T))+ 1 mm 3(1:)>5.. iiiiiiiiiii tETiiiiiiiiii Ex. :4: : :Var1a'ncc swap 3 3 PM thncfl b “hisforid 4f: rem 3 3 ’ ’ 5 5 55 . : on. an: Jada or efuck duty: : [Qt-J : : : t; . . '2' daig $.‘mejn‘d V ‘T‘ mhxrftj K strike / . idea :7 dz: : S: :15 volafifle durinj : [0,Tjij H rs +1435: : i i i :: :ccnmk rs : I’m—dad for major stacks am! 37%!) :wxdccc; : : : The: 30413: : :vamncc sewn? on He: $19500: index . . . . . . . . . : :35 - cal/ed - Ha: le : comrade : Manama 1W); i i i 3 3 3 . No cash Fromm!)de ML 0 -. K, defammed. 0+ i=0 1‘0: : , , , Mk5: wmmg imtw 0 +5 : ibaHa: i Piaghh‘q ' ' ' ' ' ' ' ...
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L5 - MSFE 2011 FOUNDATIONS OF FINANCIAL ENGINEERING...

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