4.4 The Black-Scholes Model 69
EQ[f 1 ]=S 0 Φ
⎛
⎝
ln
(S 0
K
)
+
(
r+σ
2
2
)
T
σ
√
T
⎞
⎠,
which is the first term appearing in the Black-Scholes formula. We now may
interpretΦ
(
ln(SK^0 )+
(
r+σ 22
)
T
σ
√
T
)
as the probability, that the option will be ex-
ercised, with respect to the probability measureQˇ, under whichS^1 tis a mar-
tingale.