For reference, I just updated the code and plots in the article. I also did some minor changes to the text and fixed an issue with the generation of random samples, which had a small impact in the estimations.
Left some notes at the end describing these changes, along with a reference to the original version.
So I ran the analysis again using the standard MLE technique you suggested and got the following results:
- Gaussian Model: σ = 0.0473
- Cauchy Model: σ = 0.1443
Quite an improvement from the original least squares regression approach I used!
You can find the updated plots below:
- [Probability Distributions] https://imgur.com/da8dRzm
- [Option prices chart] https://imgur.com/5hey110