The name is absent



Jos muodostetaan uusi muuttuja y = (x-σ2T)/ σ4τ, joka on normaalisti jakaantunut muuttuja
keskiarvolla 0 ja Varianssilla σ2T, voidaan kaava (L2.13) esittââ muodossa

(L2.14) S Prob[y > -log(S∕K) - (r-σ2∕2)T] =

SProbf


~logGS77Q-(r~σ2∕2)Z
σ√f


VjJ- OiV l-----------ɛ=--------


Sijoittamallayhtalot (L2.12) ja (L2.14) kaavaan (L2.ll) saadaan

(L2.15) C(S1O) = SN[d1 ]- Sexp(-rT)N[d2]1 missâ

dɪ =


d2-~


log(5∕X') + (r + σ2∕2)Z∙
σ√7

ja


og(S∕K) + (r~σ2 ∕2)T
σ4τ

Yhtalo (L2.15) on Black-Scholes-hinnoittelumalli eurooppalaiselle osto-optiolle.

Myyntioptio

Myyntioption hinnoittelukaava Voidaanjohtaa edelliseen todistukseen viitaten monella eri
tavalla. Otetaan IahtbtiIanteeksi ajan hetkellâ O muodostettava portfolio, joka muodostuu
riskittômâstâ Sijoituskohteesta, osto-optiosta ja tâmân kohde-etuudesta

(L2.16) Kexp(-rT) - S + C(S1O)

Taman portfolion arvo option erâântymispàivânâ on

(L2.17) K- S(T) + Max [S(T)-K,0] - K-S(T)Jos K ≥ S(T)

OJos K< S(T) => Max [K-S(T)3 0]



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