4.4 The Black-Scholes Model 69EQ[f 1 ]=S 0 Φ⎛
⎝
ln(S 0
K)
+
(
r+σ2
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.