# Significant digits in numerical derivative pricing

I am looking for examples for the number of significant digits commonly required to find numerically the price different types of derivatives.

For instance, if we have to price an American put option, what is the confidence interval and numerical accuracy required in the industry?

The only relevant question I have found on this website is this one, which requires 6-8 significant digits, and the only paper I was able to find in literature is this, which in the abstracts talks about 10-11 significant digits.

Is there a widely accepted standard on this? Can we have some examples?

The reality is that there is no standard on the number of significant digits, as it largely depends on the use case.

For trading purposes it depends again on the situation:

• if you are expressing the price as a %, then it's common to express with bps accuracy, where 1bp = 0.01%
• if you are expressing the price in bps and you really need precision, then you would usually add one more, to 0.1bps (e.g. 54.6bps)
• if you are expressing the price in \$terms, then it's customary to round to next \$10 or even \$100 (depending on the notional of the trade), too much precision is simply not worth it for a few dollars vs a book trading millions of \$ per day

If you are pricing for academic purposes again largely depends on what you need. I would personally not bother for more than 5 digits (unless the price is very small in abs terms). A better way to do this could be to round to 0.0001% of you price.

Something similar is for confidence intervals, as it's not really about the precision but on how large they are vs the price, consider for example $$13.5 \pm 0.1$$ vs $$0.15 \pm 0.1$$. The first is a good price while the second is not precise at all

• This is a very good answer, though it is worth mentioning that in derivatives pricing there are some counterexamples. Notably, far in-the-money european-exercise options have an intrinsic value that is very high compared to the optionality value that the Monte Carlo scheme is trying to estimate. Jun 27, 2022 at 14:43