Implied Volatility Research: Models and Further Reading

Summary

This discussion concerns a research project comparing historical, implied, and stochastic volatility approaches for forecasting future volatility. The researcher has implemented several historical-volatility estimators, including moving and exponential averages, ARCH and GARCH, and a regression approach, alongside Newton–Raphson implied-volatility calculation and the Brenner–Subrahmanyam approximation. They ask for another model or relevant papers to explore, mentioning Bachelier as one possibility.

The response recommends studying the work of Jim Gatheral and Peter Jaeckel as a route into deeper research on volatility modeling, with the possibility of contacting them about current research. It does not explain a specific model, provide citations to particular papers, or offer empirical comparisons. Its value is therefore as a pointer for further study rather than a self-contained method or evidence-based assessment; the reader would need to consult outside materials to evaluate models or their forecasting performance.

Key ideas

• The project distinguishes historical, implied, and stochastic volatility as separate modeling approaches.
• Several historical estimators and two implied-volatility methods have already been implemented by the researcher.
• Bachelier is raised as a possible additional model to implement.
• The response points to the work of Jim Gatheral and Peter Jaeckel for further study.
• The discussion gives research direction but no model details, paper references, or performance evidence.

Tags

# Implied Volatility Models


# Implied Volatility Models












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.

## Answer by will (score 3)

https://quant.stackexchange.com/a/66067

Not a complete answer persay, but two authors who i have great respect for in this field are Jim Gatheral and Peter Jaeckel.

If you want to do a serious bit of research on this topic, i'd suggest that you try to read and understand all of the work of both of them. Even better if, after reading and understanding their work, you're able to contact either/both of them to see what they're currently looking at and see if there is anything you can collaborate with them on.

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