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Choosing Numerical Precision for Derivative Prices

Article Quant Q&A · Author: asdf
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Summary

The document asks how many significant digits numerical derivative pricing should deliver, including for products such as American puts. Its answer is that there is no universal industry standard: suitable precision depends on how the result will be used and how the price is expressed. For trading, percentage quotes may be stated at basis-point precision, while basis-point quotes may need a finer decimal when precision matters. Dollar prices can be rounded according to trade notional, since very small differences may be immaterial for large positions.

Academic calculations may call for different precision, and the response offers a personal view rather than a formal standard. It also argues that confidence intervals should be judged relative to the price: the same absolute interval can be meaningful for a larger price and uninformative for a small one. No derivative-specific benchmark or evidence survey is supplied, so users should select precision based on the application and the scale of the result.

Key ideas

  • There is no broadly accepted significant-digit requirement for all derivative pricing tasks.
  • Useful precision depends on whether a price is quoted as a percentage, in basis points, or in dollars.
  • Dollar rounding can be considered relative to the notional and practical importance of the trade.
  • Confidence intervals should be assessed relative to the price magnitude, not only by their absolute width.
  • The suggested academic precision is a personal judgment rather than an industry rule.

Tags

Derivatives pricingOptionsStatisticsRisk management
Full text
# Significant digits in numerical derivative pricing


# 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?

## Answer by apocalypsis (score 3, accepted)

https://quant.stackexchange.com/a/71380

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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.