The asian option pricing isn't such as good one. Check out Asian pricing through PDEs and Crank-Nicholson MethodVecer's Paper at Columbia U.

QuoteOriginally posted by: pb273A couple of years ago, Longstaff & Swartz came out with a technique called MC with Least Square Regression (can also be used with QMC). It vastly improves the accuracy and number of paths required for MC/QMC. I think it still available on their website. It is also "less noisy" than usual MC/QMC.Yes i have seen this paper on this forum (can someone tell me something we can't find on Wilmott? ).I have also found another paper by Barraquand and Martineu which espouses on higher dimensional securities.

try this link for the Longstaff paper: MC with LSR. my implementations of the paper gave far better results than the authors have in the paper. it seems like you need a very good accurate algo for matrix inversion - otherwise errors creep on exponentially.quantie, where is the Barraquand and Martineu paper ?

QuoteOriginally posted by: PatUnless it's a one off deal, never use Monte Carlo if you have a sensible altenative: it's slow and noisy. It does not handle mulitple exercises well (Americans or Bermudans), one must take care to use the same paths when calculating the Greeks (and Greeks always need to be calculated), and one has little assurance of the size of the error [...] 1. "slow and noisy" : indeed using MC to evaluate 'simple' payoffs is unusful; however, for some complexe or / and path dependent payoffs the trade off is " slow v.s. accurate "(I let you guess my choice ! ). And of course there are various refinements of the MC that allow for much more flexibility and accuracy...(there is a lot to say, but it's a huge field !). Moreover, all depends on the way you formulate your problem (direct SDE discretisation / transformed dynamics ...) and also on how you implement it (algorithmically speaking).2. Multiple exercises : Are you thinking about some specific issues? I'll be interested in identifying some limitations (of the use of the MC in such cases), because I'll probably have to work on the subject at some point...thanks. Regards.

Collector and Rector, For your greeks computations, have you ever tried to use Malliavin Calculus MC ?- and All, any impressions to share on this subject?

Posted this elsewhere and thought this was a logical thread too:I am trying to establish properties of MC simulation and how to interpret its expected value scenario, or the average of all the individual iterations of the simulation. I am trying to explain to a colleague that we can look at th expected value of a simulation and use it to draw conclusions about the process we are trying to simulate - in this case, equity prices. My point is that the expected value of the simulation gives us our simulation's probability weighted expectation of the underlying. We can compare the E(X) from the MC to an actual equity price distribution to see how well the MC performs (again, assuming we are simulating the same equity). Here's my thoughts: Let's assume we are trying to compare the ability of a particular Monte Carlo model to accurately forecast forward looking daily vol. The model takes 365 days and computes 1,000 iterations of the daily price based on some distributions. To determine how well-calibrated the model is, I would compare the expected value of the simulation since it represents the probability weighted expected outcome for each day, to some actual series from the past. To keep it simple, I plan on comparing simple prices (not returns or log prices) to determine whether or not the Monte Carlo is doing a reasonable job of predicting both extreme values and daily volatility. Let's assume I find the following descriptive statistics:SIMULATION E(X)Mean Price = $55.00Standard Deviation = $8.80Skewness = 1.17Kurtosis = 3.06Daily volatility = 65%ACTUAL PRICESMean Price = $55.00Standard Deviation = $30.00Skewness = 20.00Kurtosis = 150Daily volatility = 150%Again, recall that I am using the arithmetic mean of the 1,000 daily simulations to represent the expected price on each of the 365 days. It is my opinion that since the E(X) embodies the probability weighted expected outcome for each hour, then it should contain the information that establishes volatility over the course of the year, as well as extreme values. Comments????

QuoteSlow and noisy?Quotecouldn't you do Bootstrapping to get CI for your calculations, with the rise of computing horsepower , i'd think MC is the way of the future The rise in computing horsepower has been neatly cancelled out by the rise in C++Put it this way: diffusion problems come up in many, many fields: fluid mechanics, heat transfer, chemical reactor dynamics, ground water flow, hydrodynamics, aerodynamics, .... In any of these fields, it is VERY rare to use Monte Carlo if one can do the calculation by finite differences/elements or some other means.What's different about finance?

QuoteOriginally posted by Pat: What's different about finance? ------------------------------------------------Dimensionality?