ASM 7.7

St lognormal
S0 = 45
Alpha = .15
Sigma = .2
P(St < 40) = .1
Find all t

No problem, how hard can this possibly be?

Pr(St < K) = N (-d hat 2), where d hat 2 = d hat 1 - sigma root t, where d hat 1 = ln(So / K) + (alpha - delta + .5 sigma squared) t, all over sigma root t)

Therefore, Pr (St < 40) = .1 = N (- ln (45/40) - (.15 - .5(.2^2))t all over .2 root t)

... what?

Where did the - sigma root t go

All this equation is is N (- d hat 1)


ASM 7.7