# MonteCarlo option pricing error estimate

Consider the problem of pricing an option via MonteCarlo with 10000 simulations. If the variance of the simulation is 100, which is the MC estimate of the error on the price?

• The confidence interval for the estimator $\hat{C}$ is given by $\hat{C}\pm z_{\alpha/2}\frac{s_C}{\sqrt{N}}$ where, in your case, $N=10,000$ and $s_C=10$. – Kevin Feb 24 at 20:51
• The options for the answer are: 1) 0.001 2) 0.01 3) 0.1 4) 1 5) 0.0001 – Pietro Scaglione Feb 24 at 20:54
• Based on your comment, I would say 0.1 – Pietro Scaglione Feb 24 at 20:56

$$\frac{\hat{\sigma(M)}}{\sqrt{M}}$$
where M is the number of simulations and $$\sigma$$ is the estimated standard deviation $$(\sqrt{\hat{\sigma^2}})$$ of the specific simulation run. The “ $$\hat{}$$” denotes that it is the estimate.