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Volatility by Adam S. Iqbal

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CHAPTER 3The Basic Greeks: Theta

The Greeks are a set of quantities that describe the sensitivity of the price of an option contract to changes in the values of the parameters or variables upon which that contract depends. We already met one of the Greeks in the previous chapter, namely delta images. There, the variable was the spot level.

More precisely, the Greeks are partial derivatives (in the calculus sense) of the option value with respect to variables such as time, the spot level, and the level of volatility, among others. They are the most important quantities to understand for practical options risk management.

One of the main advantages of thinking in terms of Greeks, rather than thinking about the dynamics of individual options, is that Greeks are additive. Consider images. If the trader owns images options, each with delta images, then the amount of spot that the trader must transact in the market to be delta hedged is simply minus the sum of the deltas arising from each individual option, −images. The ...

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