I'm reading this paper link and have came across the below statement. Can someone shed some light on it.

"The approach we propose here builds on smoothing rather than interpolation. Therefore, the input data do not need to be arbitrage-free." Thanks you.

  • $\begingroup$ famous paper, but more context is helpful. $\endgroup$ Commented Apr 19, 2017 at 21:02
  • $\begingroup$ I was unable to understand how interpolation and smoothing techniques behave in a arbitrage free world. why smoothing doesn't require arbitrage free data. The point you made sense to me. Thank you :) $\endgroup$ Commented Apr 21, 2017 at 6:34

1 Answer 1


I think they mean that by interpolation, the smile goes exactly through the implied vols of the raw market data. By smoothing, it means they are attempting a best fit subject to arbitrage constraints and the fit may not actually go exactly through the raw vol data points.

Disclaimer - I only skimmed that section of the paper rather than reading thoroughly.

  • $\begingroup$ Exactly: by going through the specified raw data points interpolation is going to preserve arbitrage possibilities (if any) at those points. By smoothing you can achieve an arbitrage free output from an arbitrage prone input. But you lose the "exact fit" property that interpolation has. $\endgroup$
    – nbbo2
    Commented Apr 19, 2017 at 21:28
  • 2
    $\begingroup$ ...also worth adding that smoothing should generally be preferred in all cases besides side of the barn approximations. The raw data can give you unrealistic shapes simply due to bid ask noise (especially on the wings) - in addition to the fact that raw data can simply be very wrong very easily - the smoothing helps to detect bad data points so you can scrub them and make a proper vol surface without the garbage - ahh the details of vol surfaces - a pain in the ass. $\endgroup$ Commented Apr 19, 2017 at 21:35
  • $\begingroup$ Thank you very much @noob2 and @ FinanceGuyThatCantCode. This is my first question on stackexchange. I really appreciate you guys taking time to answer my queries. $\endgroup$ Commented Apr 21, 2017 at 6:32
  • $\begingroup$ @FinanceGuyThatCantCode what do u mean by wings in ur explanation? yes it's a pain in the ass. I want to replicate the Fengler paper and im finding it a real pain to get into details. I posted one few more doubts of the same paper, if you don't mind would you guys take a look. [link] (quant.stackexchange.com/questions/33803/…) $\endgroup$ Commented Apr 21, 2017 at 7:08
  • $\begingroup$ "the wings" = at Strike Prices far away from ATM (on either side). Jargon sometimes used by traders. $\endgroup$
    – nbbo2
    Commented Apr 21, 2017 at 12:06

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