Choosing Volatility Models and References for Exotic Option Pricing
Summary
The document surveys references for learning local, stochastic, and local-stochastic volatility models in the context of equity derivatives and exotic options. The recommendations span theory-focused treatments, practical implementation material, and introductory explanations. Topics mentioned include the Dupire local volatility model, stochastic volatility, jump models, exotic option pricing, and numerical methods.
The responses distinguish the books by their emphasis and depth. Some are described as useful for practical application and numerical schemes, while others give more theoretical coverage or build intuition with relatively little mathematical or implementation detail. One response notes that a standard volatility text also covers jumps, default risk, barriers, and volatility derivatives, but may provide limited treatment of Greek calculations. These are recommendations rather than a technical comparison of model performance: the document provides no pricing examples, empirical evidence, or complete guidance on hedging and Greek derivation. Readers should choose a reference based on their mathematical background and need for implementation detail.
Key ideas
- Local and stochastic volatility models are distinct frameworks for describing option-implied dynamics.
- Local-stochastic volatility models combine features of both approaches.
- Recommended study material ranges from intuitive introductions to mathematically detailed and practical texts.
- Some references cover jumps, barriers, and exotic options, while depth on Greeks varies.
- The document offers book recommendations rather than evidence comparing model accuracy or hedging outcomes.
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Full text
# What is the best book to learn about local vs. stochastic volatility, modelling and pricing of Exotics? # What is the best book to learn about local vs. stochastic volatility, modelling and pricing of Exotics? I am starting to delve into the world of Exotics and I am trying to find a rigorous yet understandable book that covers both mathematically and qualitatively (especially mathematically) the following aspects: - difference between local & stochastic volatility models, upsides and downsides of each method - derivation of the price from the diffusion process obtained - derivation of the greeks from both local and stochastic models (or a combination of the 2 if both are used) - jump diffusion models - hedging If no book is available, I would be happy to go through any other type of material (e.g. paper or link to a webpage). ## Answer by jherek (score 3) https://quant.stackexchange.com/a/46661 Such a question really invites me to recommend my own book Applied Quantitative Finance for Equity Derivatives, which you can buy on Amazon. The book devotes 200 pages to the subject of volatility. It covers the Dupire local volatility model, along with tricks that are required to apply it in practice. It also covers stochastic volatility models, and local stochastic volatility models. Always, the focus is on how to apply those in practice, up to the numerical schemes details. Now, Jim Gatheral The Volatility Surface is also a good book on the subject, more on the theoretical side. Another more recent book that comes to mind is the one from Lorenzo Bergomi Stochastic Volatility Modeling. It may be a bit heavy on maths, and less on the practical side. Finally a more lightweight reading is The Volatility Smile by Emanuel Derman. It focuses on giving an intuitive understanding of the various volatility models. The intended audience is more someone who does not know much about quantitative finance and would like to understand (in some details) what is exactly a local volatility model or a stochastic volatility model. The book tries to be not too mathematical. As a consequence, it presents the models in a very superficial manner. If you want to implement the models, it is clearly not the right book. ## Answer by Kevin (score 1) https://quant.stackexchange.com/a/46631 A standard book in the volatility literature is Gatheral (2006). The book begins with stochastic volatility, llocal volatility and the Heston model. Then he adds jumps and default risks. He concludes with barrier options, exotic options and volatility derivatives. He includes many tables and graphs and writes rather well. The only downside is that he does not dive too much into computing Greeks.
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