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An Introduction to Options Trading by Frans de Weert

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Chapter 4
IMPLIED VOLATILITY
Although implied volatility is a relatively easy concept it is usually thought to be complicated. This is because things can get confusing. Implied volatility is not just a theoretical concept, it also depends on the simple market phenomenon of supply and demand. Before implied volatility is explained in more detail, volatility will be elaborated on.
 
As mentioned earlier volatility is a measure for the movement of the stock price. To be precise, it is the standard deviation of the natural logarithm of the returns of the stock price. Although this is the official definition, it is more important to understand which time period this volatility relates to in the Black-Scholes formula. The answer is of course simple, it is the volatility of the stock price during the term of the option. It is simple, but it is good to be aware of this fact, since this implies that whenever an investor wants to buy an option he does not know what the volatility will be during the term of the option. This, in turn, makes it impossible for him to calculate the fair price of the option. However, he can try to estimate this volatility by looking at what the volatility has been so far, the historic volatility. Although there are techniques to estimate the volatility accurately, he will never be able to say with certainty what the volatility will be during the term of the option. In fact, from all the variables the Black-Scholes formula uses to determine the price of an option ...

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