I'm seeing levels of -12% of market strangle vol at 25 delta for AUDJPY at 20Y onward that is causing havoc with my pricing routines, the 10 delta market strangle is trading around -6% which is again quite negative. Is this level of market strangle vol realistic as the smile becomes extremely concave and possibly arbitrageable?

To be precise with FX conventions, my delta convention is forward delta and the ATM strike is ATMF with vol around 15%.

  • $\begingroup$ I assume your smile is concave? I think this happens if the underlying is expected to make a big jump either up or down due to some event. You could back out the probability distribution and observe that it is bi-modal and assess whether or not you think the markets assessment is reasonable. $\endgroup$
    – roz
    Dec 9, 2019 at 19:04
  • $\begingroup$ The problem is the interpolation method for the smile in the market strangle solver doesn’t allow for such a concave smile, I’m using SVI or SABR. Perhaps polynomial delta would work but how the distribution will look in the tails is another problem? $\endgroup$ Dec 10, 2019 at 7:27
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    $\begingroup$ Hmmm. I know that a concave smile would imply a platykurtic (thin tailed) distribution. This thread may help you: quant.stackexchange.com/questions/31368/… . If you look further down in the post and read the Gatheral SVI paper or the SABR paper you can see that those models can possibly generate arbitragable smiles. $\endgroup$
    – roz
    Dec 10, 2019 at 16:40
  • $\begingroup$ Also look on page 28 of this slide presentation where non arbitrage bounds on the slope of the implied volatility surface are given. If the slope of your models surface is outside these bounds then you may be able to arb it. $\endgroup$
    – roz
    Dec 10, 2019 at 18:24
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    $\begingroup$ Yup here it is: itf.fys.kuleuven.be/~nikos/papers/lect3_smile.pdf . My bad. $\endgroup$
    – roz
    Dec 10, 2019 at 18:40


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