Hi all,I'm stuggling to come up with an answer to the question below. Perhaps I'm thinking about it in the wrong way, and so any advice, pointers to literature etc would be much appreciated.We have a product that pays-off at time T, dependent on the level of an equity. If, at time T, the equity is 110% of its value at time 0, then it pays X. If it reaches 120%, it pays Y. At time 0, I have implied volatilities for options of tenor T, including 110% and 120% strikes. My question is: if I was to price this using MC, which volatility do I use? The 110%? The 120%? Something else?Thanks in advance,Cheers,Donal

What's the model? Lognormal B&S? Why Monte Carlo then? Looks like you have two digitals options which depend on the skew of the implied vol so you cannot use Lognormal B&S.

if you want to do with monte carlo, then you have a european option so you just have to simulate according to the terminal probability density. and you get that by breeden-litzenberger formula...ie 2nd deriv of call prices wrt strike....but if it is 2 digital options and you don't want to do MC you can get analytic price by taking limit of call spreads