Option pricing using Local vol

[gver]

if i have two options, lets say 80% and 100% calls, and i use MC to price it with my local vol surface available then the vol chosen depends purely on where my simulated spot lies and the remaining time to maturity .. assuming i save my random nums and evolve the 80 and 100 call spots using the same then in both cases then i get the same evolution of S .. hence the vol used wld be the same in both the cases .. isnt this wrong, i mean where is the skew effect .. can u help me with what am i missing here .. thanks

 

[vertigo]

it is impossible to understand what you have written. 80% and 100% calls? what? you mean regarding at the money strike? Dupire LV does capture skew..

so say payoff 1 is f_1 = max(S_T-K_1,0) with IV(K_1) at t_0 and payoff 2 is f_2=max(S_T-K_2,0) with IV(K_2) at t_0. then by MC you simulate S_1, S_2, ... , S_N. You will not get the same vol, because IV(K_1) /=/ IV(K_2) at t_0 thus they will evolve differently? maybe introducing some symbols will help u