Stopping Monte Carlo simulation once certain convergence level is reached

I'm creating a Monte Carlo simulation model which I use to price an European option with various pay-off conditions, hence I can't use Black Scholes.

I want to stop the simulation once I am 95% sure I am within 1% of the true value.

To do this, I calculate the relative error (correct naming?) every 10 000 sims using:

$$Relative Error = \frac{(\sigma/\sqrt{n}) Z_{\delta/2}}{\mu} $$

Where $$\sigma/\sqrt{n}$$ represent the standard error and $$Z_{\delta/2}$$ my confidence level, so 1.96 for 95%.

μ is the mean (fair value) of the simulation.

If the relative error is less than let's say 1%, then I stop the simulation.

Is this the correct way of solving my problem?

Answer

Yes, that's an excellent approach. The only time it might go wrong is if, say, you are integrating on some extreme tail event without using importance sampling.

For example, let's say you were simulating expected loss on a portfolio of five bonds issued by the USA, Germany, Norway, Sweden and the Netherlands. After 10,000 simulations, there's a chance you might still not have generated any paths with defaults, in which case $\sigma=0$ and your algorithm would halt.