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I create a vol surface from the market and do smoothing(interpolation and extrapolation), and explicitly correct for any total variance decreasing on a given strike as we increase maturity. I create a ql.BlackVarianceSurface surface with my grid and am able to price using most quantlib engines. When I use my surface to create Monte Carlo paths using ql.BlackScholesMertonProcess and ql.GaussianMultiPathGenerator,however, I invariably get an error of the type: "RuntimeError: negative local vol^2 at strike 2167.82 and time 0.138889; the black vol surface is not smooth enough". If I create an Andreasen Huge surface using ql.AndreasenHugeVolatilityAdapter, then I get a local vol surface I can use for Monte Carlo paths. However, I want to have more control about how the surface is created so I am trying to create my own surface from the data, rather than running AH. If I poll the Ql vol surface using vol_process.blackVol(expiry, strike), I don’t find any decreasing total variance violations, so I believe something else is leading QL to say the surface is not smooth enough.

Does anyone know why QL may find the surface unsatisfactory, and anything I can do/ check for/ or change? Note I check the QL surface for both falling variance and for butterfly variations (along expiries).

thank you very much for the help

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  • $\begingroup$ by the way, I'm using QuantLib in Python $\endgroup$
    – vman
    Dec 7, 2022 at 16:34

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This is because QuantLib checks if the model you calibrated has "calendar arbitrage". https://github.com/lballabio/QuantLib/issues/1124

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  • $\begingroup$ For QuantLib local vol implementation $\endgroup$ Apr 3, 2023 at 10:26
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    $\begingroup$ Could the error message from the library be any less helpful? Or, could it be more helpful by providing more context? $\endgroup$ Apr 3, 2023 at 12:29
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    $\begingroup$ As a very general guideline, a more helpful error message might say what you wrote, but also show which specific inputs cause a problem, and by how much they might change, possibly in multiple ways, for the problem to go away. $\endgroup$ Apr 3, 2023 at 14:11
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    $\begingroup$ For example, totally making up some numbers, suppose a library can't bootstrap a swap curve from quotes: 3Y 5%, 4Y 25%, 5Y 5%. A more helpful error message might say something along the lines of, "can't bootstrap because quotes admit arbitrage - 4Y 25% and 5Y 5% imply 4 1 forward rate -250% < -100%. Arbitrage may be removed if 4Y were 15% or 5Y were 10%". making up the numbers. Further, you may want to allow market data that arises from small perturbations under risk scenarios to admit arbitrage. $\endgroup$ Apr 3, 2023 at 15:43

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