When pricing options, what precision should I work with?

Question

I'm wondering if there's any point at all in double-precision calculations, or whether it's ok to just do everything in single-precision, seeing how the difference on non-Tesla GPUs for single and double-precision calculations appears to be large.

Some of the operations where this is relevant are:

• General option pricing (BS, uses numerical approximation of cumulative normal distribution)
• Calculating implied volatility (Newton-Raphson)
• Interpolating the volatility smile (Levenberg-Marquardt)

In particular I'm interested in whether initial pricing is worth doing using a 'better' CND formula rather the one with just 5 constants in it... I know there are more precise ones with lots more constants, but I've been reticent to use one so far.

Answer 1

When you decide if the performance improvement is worth it you can add these to the downside ow using single precision:

• the result of your basic B-S pricer will eventually need to be multiplied with a notional and maybe a discount factor; For a sufficiently large notional you will see different results than the one calculated using double precision. Is that kind of a notional likely to occur in practice in your system?

• numerical stability. The straight-forward implementation of many algorithms (Newton-Raphson and probably Levenberg-Marquardt) may be unstable under the reduced precision of a single. Stable versions are slower and add complexity.

• validation. Many people use Excel or other similar software to quickly test the final results of a complex calculation. Due to the difference in precision between that and your software the results will not match, leading to head-scratching and an impossibility of validating your results.