26 lines
1.6 KiB
Plaintext
26 lines
1.6 KiB
Plaintext
Consider a $60 stock with a call option that has a 0.50 delta and is trading
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for 3.00. Considering only the delta, if the stock price increases by $1, the
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theoretical value of the call will rise by 0.50. That’s 50 percent of the stock
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price change. The new call value will be 3.50. If the stock price decreases
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by $1, the 0.50 delta will cause the call to decrease in value by 0.50, from
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3.00 to 2.50.
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Puts have a negative correlation to the underlying. That is, put values
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decrease when the stock price rises and vice versa. Puts, therefore, have
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negative deltas. Here is a simplified example of the delta effect on a −0.40-
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delta put:
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As the stock rises from $60 to $61, the delta of −0.40 causes the put value
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to go from $2.25 to $1.85. The put decreases by 40 percent of the stock
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price increase. If the stock price instead declined by $1, the put value would
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increase by $0.40, to $2.65.
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Unfortunately, real life is a bit more complicated than the simplified
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examples of delta used here. In reality, the value of both the call and the put
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will likely be higher with the stock at $61 than was shown in these
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examples. We’ll expand on this concept later when we tackle the topic of
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gamma.
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Definition 2 : Delta can also be described another way. Exhibit 2.1 shows
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the value of a call option with three months to expiration at a variable stock
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price. As the stock price rises, the call is worth more; as the stock price
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declines, the call value moves toward zero. Mathematically, for any given
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point on the graph, the derivative will show the rate of change of the option
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price. The delta is the first derivative of the graph of the option price
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relative to the stock price . |