I am doing a research project and writing about volatility modeling. The three broad basis I am covering are Historical volatility, Implied volatility and stochastic volatility. It is my aim to code and evaluate models for all of these approaches, and discuss how they can be used in predicting future volatility.
I am happy with my code for historical volatility, I have coded a variety of exponential and moving averages, implementation of GARCH and ARCH and a regression based approach from another paper I read.
However, for implied volatility I would like more content. I have coded raphson which fully works, and the simple implementation of Brenner and Subrahmanyam's proposal from 1988. I'd now like to either look at Bechelier, which I have done theoretically but not in python, or another model if anyone has suggestions of an interesting one to look at here.
Any general suggestions of new models to look at or interesting papers on the topic greatly appreciated, thanks.