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The Greeks chapter in Hull’s Options, Futures, and other derivatives book would be a good start if you have not read Hull’s. The Greeks and Hedging Explained by Peter Leoni is also very accessible and provides good coverage of the concepts. And if you prefer the traders style then you might like Taleb’s Dynamic Hedging. The title makes it sound technical ...

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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 ...

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Reposting comments as an answer: If you are doing Monte Carlo you'd have a new volatility function to use (rather than a constant vol like in black scholes) for each time and stock price from the local volatility model (It's usually written $\sigma (S, t)$). So you could use this local volatility function during a simulation regardless of the type of payoff....

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As Nap D. Lover said, here you have a list without any dividends being considered. It all depends on your model though. If you are using a stochastic volatility model or similar extensions, you get different Greeks. For the Heston model, for instance, see Chapyer 11 in here. In general however, if you have formulae including a dividend yield $q$, just use ...

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The cost of carry $b$ is, as the name says, the cost which rises when you hold this asset. For instance, if you buy a share, you cannot invest your money in a risk-free bond. Thus, the risk-free rate $r$ is part of your cost of carry. It is the cost you give up in order to be able to own this particular share. On the other hand, owning this share may give ...

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The first method assumes that the value of a floating leg at libor flat is 100. This contains an inbuilt assumption that the discount rate is Libor flat, which is an assumption that used to be made. Nowadays , we discount cash flows at Fed Funds (or Eonia in Europe), so the second method is better: first replace the floating rates by their forward rates, ...

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