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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 ...


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 ...


This is a well tackled problem in the GBM case. See Geman/Yor (1996), Pricing and Hedging Double-Barrier Options: A Probabilistic Approach. Mathematical Finance, 6(4), p. 365-378 among other references. Though in practice finite differences or MC would be used to deal with discrete dividends, local and/or stochastic volatility, etc.

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