I'm trying to verify the accuracy of my Monte Carlo method for pricing mean options. I came across this paper that supposedly gives an 'exact' solution for the arithmetic mean option (asian). It's a relatively short paper, but is it reliable?

I can't seem to reproduce the results shown in the paper and it is a simple calculation (or so I thought).

Please look at this extract from the paper (pg. 3):


I tried to put this into MATLAB, but I don't get the 0.498 mention, instead I get 0.5004. Does this paper make a mistake? When I compare this solution to my Monte Carlo, the error doesn't seem to get smaller as it should (by LLN etc.).

Any pointers in the right direction? Here is my attempt to implement the formula given in the paper into MATLAB:

MATLAB function

  • $\begingroup$ "When I compare this solution to my Monte Carlo the error doesn't seem to get smaller as it should (by LLN etc.)". I am not sure what you mean by this sentence? $\endgroup$
    – Sanjay
    Mar 22, 2019 at 15:31
  • $\begingroup$ Thanks Sanjay...I was hoping to simulate the Asian option using a discretisation method and a large number of simulations for a good approximate. But the error term does not truly converge and remains around 0.028. $\endgroup$
    – Henry P
    Mar 22, 2019 at 15:47
  • $\begingroup$ How do you measure you error? Remember to use 0.5004 as exact solution not NOT 0.498. $\endgroup$
    – Sanjay
    Mar 22, 2019 at 15:51

1 Answer 1


The paper is reliable and the formula is correct. However as you mention yourself there is an error. $$ \frac{\log \left(\frac{e^{0.01}-1}{0.01}\right)}{0.01} = 0.500417 \neq 0.498 $$


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