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I have implemented some Monte Carlo and FDM code. I can then get greeks by bumping.

I am comparing to to exact formulas of price + greeks, and am wondering how many decimals of accuracy I can expect for reasonable inputs (say, 100.000 paths and 250 steps in MC, and 2000x2000 gridsize in FDM).

For example, take FDM and estimating the delta by bumping: I am personally getting 0.5281 in delta from exact formula, and 0.5298 from FDM by bumping, so about 2 decimals worth of accuracy. Is this normal?

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This depends on quite a few other inputs. If you're comparing deltas, what's the volatility of the underlying and the moneyness of the derivative (whether call, put, or something more exotic). I've done valuations that need 10 million simulations (5x out of the money options with 10 years until expiration) and others where 10,000 is perfectly sufficient (at or in the money with a short life).

That delta seems fair under common circumstances and 100k paths (since the option ,I presume something similar to a call option, is fairly near the money with a delta ~=0.5).

You can always run this a couple times with a different seed and see if the result changes (it should, but centered around the actual value). Additionally, as you increase or decrease the number of paths, the standard error will change by a factor of $\frac{1}{\sqrt{n}}$.

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