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.
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