5 The BlackScholes formula for pricing European call options is Vs; T s flogs=k r...

5 The Black–Scholes formula for pricing European call options is V…s; T† ˆ s Φ‰flog…s=k† ‡ …r ‡ 1=2 σ2†Tg=σ

p TŠ  keτTΦ‰flog…s=k†

‡…r  1=2σ2†Tg=σ

p TŠ

where Φ…x† ˆ …2π†1=2 ∫x

1exp …y2=2†dy, the probability that a normal distribution N(0, 1) has values less than x, then one may calculate that V0=V(s, T).

Consider the change of variable v ˆ …x ‡ 1=2σ2T†=σ

p T;

and use it to establish the common form of the Black–Scholes formula, namely, V0 ˆ sΦ…α ‡ σ

p T†  keτTΦ…α†