The Mathematics of Arbitrage

(Tina Meador) #1
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.

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