Recommended References for Local and Stochastic Volatility Models
Summary
The document collects learning resources for someone starting with volatility modeling, especially local volatility and surface calibration. It points to a practitioner book and lectures, a thesis focused on calibrating a local volatility surface, and a short interpolation paper used as a reference for calibration methods.
It also highlights a discussion comparing piecewise constant and piecewise linear interpolation, noting that the latter may help avoid volatility blowups in some cases. A further stochastic volatility text introduces local volatility in its opening chapters, while an OpenGamma article covers implied volatility interpolation and local surface construction. These are recommendations rather than a unified tutorial or comparative evaluation; the contributor describes some material as difficult or brief, and provides no systematic evidence about which resource is best for a beginner.
Key ideas
- Local volatility references can cover both model foundations and calibration of the volatility surface.
- A practitioner text and its lectures are presented as standard resources, though some sections may be unclear to beginners.
- A thesis is recommended for a fuller treatment of local volatility calibration.
- Piecewise linear interpolation is suggested as an alternative to piecewise constant interpolation to reduce volatility blowups in some cases.
- Some advanced references may need to be paired with more introductory material.
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# Book/ Articles recommendation for Volatility models # Book/ Articles recommendation for Volatility models I am looking for references on volatility models. I want to gain more insights on these models but have a little background as of now. Thus, looking for references that can pick the topic from basics and build the concepts gradually. For e.g. a reading that starts from basics of local vol and describes about the calibration process too. Thanks in advance ## Answer by Jesper Tidblom (score 10) https://quant.stackexchange.com/a/55147 I have also currently started to learn about the subject. This is some of the material I have encountered: Many people recommend the book "The Volatility Surface: A Practitioner's Guide" by Jim Gatheral. It is a standard reference in the area (even though I personally found it a bit confusing and a bit unclear at some parts). The author also have some lectures in the area online one can download for free. I found a nice master thesis that explains a lot about the calibration of the local volatility surface called "Calibrating the local volatility model" by Lykke Rasmussen. It can be downloaded online as well. A standard reference in the area of calibrating the local vol surface is also the article "volatility interpolation" by J. Andreasen and B. Huge. It is very brief though and do not elaborate on details, so it is a good idea to use other references at the same time. The blog "Chase the devil" and the article "don't stay flat" by Fabien Le Floc'h contains a nice comment on the article of Andreasen, Huge about the interpolation used and suggest piecewise linear interpolation instead of piecewise constant interpolation as in the mentioned article, to avoid volatility blowups in some cases. There is also a book called "Stochastic volatility modeling" where you can find the first two chapters for free (about local vol for among other things). You find it here: https://www.lorenzobergomi.com/contents-sample-chapters. OpenGamma also have an article called "local volatility" about interpolation of the implied volatility surface and construction of the local volatility surface. It seems a bit too advanced for me at the moment, but it might be a good reference.
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