Choosing Numerical Pricing Accuracy by Its Practical Impact

Summary

The document asks how close a numerical option-pricing method must come to a benchmark before its accuracy is adequate for practical use. It uses the Black–Scholes call price as an example and imagines a situation where a slower exact calculation motivates finding a numerical alternative. The central issue is how to choose an acceptable error tolerance, rather than how to implement a particular algorithm.

The author points out that the answer depends on the real-world consequences of mispricing and does not offer a threshold, a measurement procedure, or empirical evidence for one. As a result, this is a useful framing of model validation and numerical accuracy, but it leaves the decision unresolved. Readers would need to connect pricing error to their own use case, such as valuation sensitivity or downstream trading decisions, before setting a tolerance.

Key ideas

• A pricing algorithm's accuracy should be judged against a benchmark such as an exact option-pricing formula.
• The document frames acceptable error as dependent on the real-world consequences of mispricing.
• It offers no specific tolerance, validation method, or evidence for a universal accuracy threshold.

Tags

# How good is a "good accuracy" in pricing?


# How good is a "good accuracy" in pricing?












Say you want to test various numerical algorithms for purposes of pricing.

How close do you need to be to some benchmark value (the "actual" price) for your accuracy to be good?

Say I am trying to approximate the Black Scholes formula for a call option price. How many digits of accuracy do I need to get from my numerical algorithm for it to be acceptable and maybe even usable in practice? Obviously you wouldn't use it since BS-formula is quick and exact, but imagine if for some reason it took a long time to use the BS-formula so that we start looking for numerical alternatives...

I find this hard to answer since the answer would seem to depend on the real-world consequences of the mispricing, which I feel like I am in no position to quantify.

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.