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)
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