The name is absent



Kaavassa (L2.11) on kâytetty apuna normaalijakauman tiheysfunktiota ja yhtâiossâ (L2.8)
olleen maksimointifunktion termit on kerrottu diskonttotekijâllâ exp(-rT). Yhtalon (L2,11)
viimeinen rivi voidaan vielà kehittâa Seuraavasti

(L2.12) Sexp(-rT) f     —r~ exp(--~)dx -

,i 2 σ∖2πT 2cτ7^

Л. 2

Sexp(-rT) Probfx > -log(S∕K) -(r-σ2∕2)T] =

ς r TAD M x ∣og(S∕∕0 + (r-σ2∕2)7'

Sexp(-rT) Probf--7= <-----------τ=---------]=

σ√ 1          σd l

Sexp(-rT)N[- log(5∕^) + (r~σ3∕2)71 ]

σjτ

Merkinta N[.] viittaa Standardoituun normaalijakauman kertymâfunktioon. Myos toinen rivi
yhtàlôstâ (L2.11) voidaan kehittâa hiukan toisenlaiseen muotoon

1                 X *         ɔ

(l2∙13)s    ∫     —≡=veχP(-τ-⅛--^ + x)a⅛ =

c j , σ√2τr7       2σ"/    2

6 σ

" ɪog(- )-('ʃ-


........-,r. (x~
2σ~T


- 2xσ2 T + σ4 T2 )]√x =


1 r (x-σ2Γ)21j
—7= exp [..  Их

σ-χ∣2πT        2σ2T




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