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When pricing a european option by monte carlo over 30 days for instance, what's the difference between one big 30 day jump vs 30 one day steps?

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You may want to consider reposting your question on which is specifically devoted to Quantitative Finance. – Andrey Rekalo Mar 31 '11 at 13:06
up vote 1 down vote accepted

You are in effect replacing many detailed paths by their average effect. This changes the answer since pricing options involves applying the non-linear $\max$ or $\min$ operators. If you are trying to compute the answer corresponding to a continuous time model, then you have to take a large enough number of steps.

It may help your intuition to draw two binomial tree models, one with one period and one with two periods and solve them by hand.

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Theoretical option prices are linear averages over paths, in a suitable measure. So there is not necessarily a problem with the idea of replacing an ensemble of detailed paths by an average. – T.. Oct 26 '10 at 5:08

European options have an efficiently computable deterministic answer in both the continuous time and discrete lattice (binomial tree) settings. Unless you are outside the Black-Scholes framework, random walk simulations are needed only for path-dependent options.

If you are asking about the accuracy of the discretization, it is not only a function of the number of steps. Both the "time" and "money" coordinates are discretized, and the random walk answer may not converge at all unless the time and price steps are sized correctly relative to each other.

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