QuoteDecreasing dt and/or increasing NSIM means nothing.We do, in fact, have some theory for this; see "Efficient Monte Carlo Simulation of Security Prices" by Darrell Duffie and Peter Glynn.PDF:
http://www.darrellduffie.com/uploads/pu ... pdfQuoteWe can also view the result in terms of the asymptotic relation between the number k of Monte Carlo simulations and the size h of a time interval.The theorem implies that, asymptotically, it is optimal to have k increasing at the order of h^(-2p).For instance, with the Euler scheme (p = 1), the number of simulations should quadruple with each doubling of the number of time intervals.With a second-order scheme, the number of simulations should be on the order of the number of time intervals to the fourth power and so on.Similarly, with an optimal Euler scheme, asymptotically speaking, for each doubling of the number of time intervals the root-mean-squared estimation error is halved.For an asymptotically optimal second-order scheme such as the Milshtein (1978) scheme (for N = 1) or Talay (1984, 1986) scheme (for N >= 1), for each doubling of the number of time intervals, the root-mean-squared estimation error is reduced by a factor of 4.The option pricing example shown in the next section has estimation errors for finite samples that are consistent with this asymptotic error behavior. Numerical examples given by Kloeden and Platen (1992) are also consistent with this predicted behavior.There's a but though: In general, the optimal constant of proportionality is not known. That being said, in some cases it can be found experimentally, AFAIR there's also been some research with an analytic tretment.