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An Introduction to Options Trading by Frans de Weert

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Chapter 5
DELTA
Delta measures the sensitivity of the option price to the stock price while all other variables remain unchanged. Mathematically, it is the derivative of the option price with respect to the stock price. So, if the delta of an option is 0.5, it means that – if the stock price increases by $1 – the option price increases by $0.5,7 and if the stock price decreases by a small amount the option price decreases by 50% of that amount. If delta is negative the reverse holds. Suppose an option has a delta of – 0.5. In this case, if the stock price increases by $1 the option price decreases by $0.5, and if the stock price decreases by $1 the option price increases by $0.5. The delta of a put option is negative, since the price of a put option decreases as the stock price increases. For a call option the reverse holds, since the price of a call option increases as the stock price increases. The delta of a call option is between 0 and 1, and for a put option it is between – 1 and 0. It was argued that the delta of a call option had to be greater than 0. But why does the delta of a call option have to be less than 1? To answer this question it is important to know what comprises the price of a call option. This price has an intrinsic8 part and an option part. It has an intrinsic part since the price of a call option on a non-dividend paying9 stock is always at least as much as the intrinsic value. After all, an American call option can be exercised immediately to get a payoff ...

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