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training_data/curated/text/2e697441163b73813e26db7221d79004de9851532415f1c580ab0916ea8a7769.txt

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+Each $1 increase in the stock shows an increase in the call value about
+equal to the average delta value between the two stock prices. If the stock
+were to decline, the delta would get smaller at a decreasing rate.
+As the stock price declines from $60 to $59, the option delta decreases
+from 0.50 to 0.46. There is an average delta of about 0.48 between the two
+stock prices. At $59 the new theoretical value of the call is 2.52. The
+gamma continues to affect the option’s delta and thereby its theoretical
+value as the stock continues its decline to $58 and beyond.
+Puts work the same way, but because they have a negative delta, when
+there is a positive stock-price movement the gamma makes the put delta
+less negative, moving closer to 0. The following example clarifies this.
+As the stock price rises, this put moves more and more out-of-the-money.
+Its theoretical value is decreasing by the rate of the changing delta. At $60,
+the delta is −0.40. As the stock rises to $61, the delta changes to −0.36. The
+average delta during that move is about −0.38, which is reflected in the
+change in the value of the put.
+If the stock price declines and the put moves more toward being in-the-
+money, the delta becomes more negative—that is, the put acts more like a
+short stock position.
+Here, the put value rises by the average delta value between each
+incremental change in the stock price.
+These examples illustrate the effect of gamma on an option without
+discussing the impact on the trader’s position. When traders buy options,
+they acquire positive gamma. Since gamma causes options to gain value at