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Handle Floch-Kennedy SABR parameter limits without cancellation - #3045
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Signed-off-by: Tianlang (Jackie) Chen <305351710+jackiectl2@users.noreply.github.com>
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Closes #3018.
Use the analytic limits
y = log(k/F)at beta = 1 andDint = -y/alphaat nu = 0. Both parameter values are allowed by the SABR model, but currently produce NaN away from the near-ATM Taylor branch.For nonzero values, evaluate the power difference with
expm1and rationalize the distance logarithm before usinglog1p. This also avoids the cancellation near those limits, without choosing an arbitrary parameter cutoff.The regression covers the two exact boundaries, beta approaching 1, small nonzero nu, and constant volatility on both sides of the near-ATM switch. Reference values were independently evaluated at 70 decimal digits; existing published-example and ATM-smoothness tests are retained.
Validation:
QuantLibTests/InterpolationTestssuite passes.git diff --checkpasses.The full QuantLib test suite, MSVC/macOS and non-default/AAD builds were not run. No remote workflows were dispatched.