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6CO MSE RA AM athematca ( Feaance. | Lecture | lecturer : Ryan Somelly cyan. f.donnell y @ keleac.uk OL Free Hours > Tharsdays I-~2pm SS. 35 What ts Hts medule all about? —> to find the Plice (priees’ \ of inancdl olen ivatives 5 aka, contingent claims , a.k.a, Pinorctel options main module cont ta t id l. Single step binomel mode| p chesag 2 . N alti step binomsel mod el pricing 3. Crash course on Stochaste Calealas 4. Contayous Hme pricing Simple motivating exanple* Seppe we moe | price chang, af 4 Finacial asset unk a sragle peciod bi Aomiel molt | . ps lao od "eS Fo You Sgn a conteack vith me tat Leys at this Cabare tne you may buy te asvt from me for 110. Lalls Consshic He Value ES this Contract ty Vou in all poss ble states of the Rature, it the Price — increes b [2 , yen exer e your option C buy Somethits worth 120 fee only ilo) . =>» He contract 5 worth lo fa As Liture state . Tf the price Arereeses to 30, the corteatt is worth O. e/ lO what is the “Lace! value Se A x thts contract at tine ot e O Somewhyt More gunerall y + conse on asut S uth Oy no mt el mol * P Sy So I-p Sy ond Qa can Fin gat Clarm uh pay at Lancton -: f AS) hot is He fare value F V2 Ta te simple motivating Example , te combrge+ £ thet troche ne Ss called Q ucopeon Call option uth sterke K=UO. \Whut ts He paystt Panctiun & a Evuropecn call optrer. &E)= max §S-K,oh= G-k), bitrany 1s 4 pecttlis sotis tying He Flloving® i) V=0 (Free te enter I) PU, >=C) 2O (wight make prst:t’ HY PU, = O)= | (can act lose’ Wwe do nit wont acbitrege ty exist MM oar mod. Letts Try to Create one te See hat restriction, are pyded te eltminete. Hem, V= aA + BB by Ve=o => aA, +88, =o = =—- «A, # B, Vi = aA+ 2b. = «A ~ aAs om ios V. = &(Ay As 8.) 6, Suppose a >o and A, -~A,b. > 6 © “Re Then Vo =O and therefane iP(Y, >0) ?o i’) rf Vy =O they this TS aa arbibeog , => we mash have Uy <0 ft eltacagk arbtneg . nH Kar As a) No bo Aa - Ae By SO (xx bs © As eo Aw be b., @ Aah ba b, Tt You era back to He 4 Ssunptoas aboot xX >0 ond Ay Ash >> ead contle all poss bile, you vill see thet crbitnaye. ss alse elandkd by i ei Har ft Hew jotg xelty conl tory is cotistiel thn thee ts No «th bi brosg | 4 ay we 3 \Je O Tt Km 1s any megatve O nu mbt Wan hau ar bitiecg Sm we-l. @=2 | Ss 3 \ Sagpow hue a macket wit no arbitra ¢ 7 J Aa p @, A, &, Ay ey ox atroduce a thred asyt C. P/ Cw what is tie, reletion het iL Cc, Co. Cy Cy (cod A os NCA such thet thore ts shill no acbitrage*, 
