I am currently to create my own volatility smile for cryptocurrency options. I am basically reading the bids and offers and calculating the implied volatilities.

I now want to shape and parametrise my own volatility smile. What is a good way to do it? I tried the Corrado-Su Model, but I was not too happy about the results. Currently I use something simple:

$$\sigma(X) = \sigma_{ATM} \times (F/X)^{1-\beta}$$

where $X$ = Strike and $F$ = Underlying Price.

However, having only 1 parameter ($\beta$) to calibrate is a bit small.

Are there any other simple implementations to build a volatility smile?

  • $\begingroup$ Why not try the SABR vol model? $\endgroup$ – Gordon Aug 31 '17 at 17:25
  • $\begingroup$ The last time I checked the bid/offer on cryptocurrency options was huge - if you just run a naive optimisation through it it's likely going to give you all kinds of craziness, especially in the wings. $\endgroup$ – will Sep 2 '17 at 10:16

I recommend you have a look at the SABR model. Wikipedia is a great starting point to get the relevant literature.

The main advantage of the SABR model is that analytic approximations exist, which allow for a simple calibration. You just have to optimize the model parameters to fit your observed Call/Put prices or corresponding implied volatilities.

  • $\begingroup$ Thanks for your answer, but the SABR model does not help me. I am actually looking for something way more simple. I am looking for an equation which is dependant on e.g. moneyness (or log-moneyness) and one or two other variables like skew and kurtosis. $\endgroup$ – Julien Dec 1 '17 at 4:04
  • $\begingroup$ In my opinion the SABR model fits that bill quite nicely, since it allows you to control skew, kurtosis and in addition correlation between spot and volatility moves. Can you please explain precisely why you do not want to use SABR? Maybe that helps us in makeing better suggestions. $\endgroup$ – user2398678 Dec 28 '17 at 11:25

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