I am faced with the following question and my choices are down to (b) and (d). Not too sure whether the use of pseudo-numbers will improve the accuracy of monte carlo as my understanding is that pseudo will only help to achieve a certain level of accuracy faster as compared to random numbers. I am wondering anyone has any experience on how log transformations (i.e. x= LnS) will help to improve the accuracy of monte carlo ? Please advise. Thank you.Which is NOT a method for improving the accuracy of Monte Carlo simulations.(a) Antithetic variance reduction.(b) Log-transformations.(c) The use of control variates.(d) The use of pseudo-numbers.

Log transformation helps a great deal, when the payoff function depends only on the terminal value of the stock (i.e. it's not path-dependent). -- The big advantage is obvious since you have to stimulate only the terminal value, not the entire path (log transformation enables this to be done).I have seen LnS transformation in some cases when path-dependency did exist. (I didn't appreciate the utility of doing the transformation, then, because it seemed, the same simulation without log transformation would be as efficient -- same no. of steps, either way). I am myself trying to look for answer, in this case.----------------I am faced with the following question and my choices are down to (b) and (d)I believe you are already using (a) and (c) -- and that's why left with only (b) and (d) ---... I can't think of a situation where (a) and (c) won't be useful. Am I right .... or is it that (a) and (c) don't apply to problem you are considering ?

I don't see how log transformations are going to improve *accuracy* in your MC.All the others listed can improve convergence On (a) if your payoff is not monotonically increasing this can actually increase the variance of the estimator see GlassermanOn (c) the key is to pick the right weights for the c.v. and this mayn't be obvious.

I think the answer is (b) Log-transformations. It seems to be a trick question. Simulating ln(S) instead of S improves accuracy since the price movement model describes the process of ln(S). However, the idea is to use Ito's lemma to find the continuous process followed by ln(S), then discretize that continuous process, and then exponentiate the discretized process in order to get the discertization for S. Thus exponentiatal transformations are used, but not logarithmic transformations, strictly speaking.

Er. Also, ...(d) The use of pseudo-numbers.I believe that should be "The use of quasi-random numbers." I don't know what a "pseudo-number" is, and all simulated random numbers are "psuedo-random numbers." But that is a lot of nitpicking. It seems to me that (d) is still more correct than (b), the author of the question probably did mean "quasi-random."

the difference although both are algorithm generated the QMC-Quasi random numbers are deterministic equidistributedsequences the others are not.

I believe logs do improve the accuracy of monte carlo simulations. When considering the prior distribution it is often useful to think of scale parameters in terms of logs because then a scale transformation which is multiplicative will become additive in logs. Often the priors used will correspond to a flat prior using logs, (eg- "p(mu, sigmasq) proportional to 1/sigmasq" as a prior corresponds to putting a flat prior for log(sigmasq)) So based on this, taking logs to the priors will improve the simulations and lead to more accurate posterior densityI am also a little confused about what is meant by pseudo numbers in this case. pseudo meaning random? The whole idea of monte carlo simulations is that we treat the parameters as random quantities. I cant see how random numbers would improve the simulation process, basically after x number of iterations you hit the chain and stay there, then iterations and the simulations are essentially random themselves and we take averages to estimate the model and the density.