Fitting a Cryptocurrency Options Volatility Smile with SABR

Summary

The document considers how to parameterize an implied volatility smile for cryptocurrency options using observed bid and offer prices. The author’s starting point is a simple power relationship between volatility, strike, and the underlying price, but finds that its single calibration parameter offers too little flexibility. A Corrado–Su approach was also tried without satisfactory results.

The response suggests SABR as an alternative. Its practical appeal is that analytic approximations can make calibration straightforward: optimize the model parameters to fit observed call and put prices or their implied volatilities. The response does not provide a fitting procedure, parameter constraints, comparison results, or guidance on selecting among quotes. It is a brief model suggestion rather than evidence that SABR will fit a particular cryptocurrency market well; calibration quality will depend on the observed data and modeling choices.

Key ideas

• A simple power-law smile links implied volatility to strike and underlying price.
• A single shape parameter may not offer enough flexibility for calibration.
• SABR provides a more parameterized alternative for modeling a volatility smile.
• Analytic approximations can support fitting SABR parameters to option prices or implied volatilities.
• The document gives no empirical comparison or market-specific calibration guidance.

Tags

# Build Implied Volatility Smile


# 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?

## Answer by user2398678 (score 4)

https://quant.stackexchange.com/a/35872

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.