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training_data/curated/text/ee124d4dd44a835376fb26f084ebe3acc7c643e57d6e6af241783405ec65155e.txt

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