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).

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    $\begingroup$ I very much enjoyed the following book which strikes a fine balance between theory and practice: palgrave.com/gp/book/9781137335715 It covers local vol, stochastic vol, and local stochastic vol. Both plain vanilla and light exotics are covered. $\endgroup$ – ilovevolatility Jul 4 '19 at 7:03

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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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.

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  • $\begingroup$ Would you have any sample chapters or the Table of Contents for your book? It looks promising but doesn't have much info on it or reviews yet $\endgroup$ – Slade Jul 17 '19 at 12:38
  • $\begingroup$ Yes, the table of content is jherekhealy.github.io/eqd_book_toc.pdf and a more detailed presentation of the book jherekhealy.github.io/posts/… $\endgroup$ – jherek Jul 18 '19 at 13:13
  • $\begingroup$ Ah it looks interesting then. I was looking for something similar to Bergomi's book but a bit more accessible. I'll purchase once I have more money! Thanks! $\endgroup$ – Slade Jul 18 '19 at 13:29

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