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the output of an MC simulation depends on the random numbers used and if the distribution used is not too weird, after 10,000 runs you will get an answer that is distributed $$ \mu + \frac{\sigma}{\sqrt{n}} Z, $$ with $Z$ a standard normal. Here $n=10,000.$ With $\mu$ the quantity you want and $\sigma$ the standard deviation. So you won't get precisely the ...


It appears that you are plotting your analytical delta as a % of the delta of the underlying. This is why the delta converges to 100% As for the numerical delta, it could be that you are not adjusting for the DV01 of the underlying. This would explain why the numerical delta still increases as the option gets more in the money and why the distortion is ...

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