Fix SmileSectionRNDCalculator tail quantiles for smiles with fat wings - #2772
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lballabio merged 1 commit intoSep 16, 2026
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Follow-up to #2768.
With fat wings, the fixed ±5 ATM-standard-deviation strike grid can make
invcdfsaturate too early. Computing the left-tail CDF as1 - P(S > K)also loses precision.
This tabulates log-moneyness against$z = \Phi^{-1}(P(S \leq K))$ , with nodes
approximately uniform in
zand an adaptive search for the range endpoints.Each tail uses its own put or call digital, with a relative gap of
|K| * 2e-6to limit roundoff across widely varying strikes.
The
nStddefault changes from 5 to 8. This also changesGaussianCopulaSpreadEngineprices, since it uses the calculator's defaults.Five regression tests cover forward reproduction, quantile saturation,
low-ATM-volatility fat wings, spread put-call parity, and the left-tail CDF
against the analytic lognormal result.