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An Introduction to Options Trading by Frans de Weert

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Chapter 6
THREE OTHER GREEKS
In this chapter three other Greeks will be introduced – respectively, gamma, theta and vega. Gamma measures delta’s sensitivity to the stock price, theta measures the option price’s sensitivity to the passage of time, and vega measures the option price’s sensitivity to volatility.

6.1 GAMMA

Previously, in most examples concerning δ it was said that a $1 change in stock price would cause the option price to change by δ. Although in these examples this is a useful interpretation of δ, it is not totally correct. This is because δ changes even if the stock price changes by a small amount and also with the passage of time. Thus, while the stock price changes by $1, δ takes many different values. This means that it is not correct to calculate the option price change, caused by a $1 change in stock price, using only one δ-value. The right way to deal with δ is, if the stock price changes by a small20 amount, then the option price changes by δ times this amount. Since δ changes if the stock price changes, it would be nice to have a unit that measures delta’s sensitivity to stock price movements. This unit is called ‘gamma’ and is indicated by the Greek letter γ. Mathematically, γ is the derivative of δ with respect to the stock price. If gamma is small, stock price movements only cause small changes in delta. However, if gamma is large, delta is highly sensitive to stock price changes. So, an investor who owns an option with a large gamma has to adjust ...

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