I am trying to price barrier options which can have daily or monthly observations. I first calibrated by Black vols into smooth SVI vols (with linear interpolation along time in variance) to obtain arbitrage free vols.
In my initial MC implementation, I was simulating daily prices up to the option maturity by calculating the local vol using Dupire's formula on each of those dates/strikes.
But this is obviously very slow when pricing long dated options. My worry is that if I just have weekly time grids instead in my paths, I would be losing accuracy especially for the one with daily observations. And for the monthly observations, how do i speed this up since I don't really need the daily observations.