Build Implied Volatility Smile

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?

• Why not try the SABR vol model? – Gordon Aug 31 '17 at 17:25
• 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. – will Sep 2 '17 at 10:16