Take the tour ×  For a vanilla option, I know that the
probability of the option expiring in the money is simply the
delta of the option... but how would I calculate the
probability, without doing monte carlo, of the underlying
touching the strike at some time at or before maturity?
share|improve this question It seems like for a vanilla there
should be a non-simulation way to calculate this. –  glyphard
Feb 7 '11 at 22:51 This question is entitled the "probability of
touching", but the OP was asking for the probability of an
option expiring in the money. The two are not the same. Note how
many folks mentioned "stopping time" and "barriers" in their
answers. –  William S. Wong Nov 11 '12 at 5:52 @WilliamS.Wong -
the OP is about probability of touching, before expiration. Read
it again. –  glyphard Nov 11 '12 at 19:12 add comment  6 Answers
up vote 9 down vote accepted  There is a simple solution if
there is no drift, as the probability $p(x,t)$ obeys a simple
diffusion equation: $\mathrm{d}(p)/\mathrm{d}t =