45 lines
2.2 KiB
Plaintext
45 lines
2.2 KiB
Plaintext
Chapter 40: Advanced Concepts 883
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One other point should be made: The fact that gamma and delta are neutral to
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begin with does not mean that they will remain neutral indefinitely as the stock
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moves (or even as volatility changes). However, there will be little or no effect of
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stock price movements on the position in the short run.
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In summary, then, one can always create a position that is neutral with respect
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to both gamma and delta by first choosing a ratio that makes the gamma zero, and
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then using a position in the underlying security to neutralize the delta that is created
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by the chosen ratio. This type of position would always involve two options and some
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stock. The resulting position will not necessarily be neutral with respect to the other
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risk factors.
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THE MATHEMATICAL APPROACH
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The strategist should be aware that the process of determining neutrality in several
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of the risk variables can be handled quite easily by a computer. All that is required is
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to solve a series of simultaneous equations.
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In the preceding example, the resulting vega was negative: -$238. For each
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decline of 1 percentage point in volatility from .the current level of 35%, one could
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expect to make $238. This result could have been reached by another method, as
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long as one were willing to spell out in advance the amount of vega risk he wants to
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accept. Then, he can also assume the gamma is zero and solve for the quantity of
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options to trade in the spread. The delta would be neutralized, as above, by using the
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common stock.
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Example: Prices are the same as in the preceding example. XYZ is 48. There are
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three months to expiration, and the volatility of XYZ and its options is 35%. The fol
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lowing information is also the same:
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Option
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April 50 call
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April 60 call
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Price
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2.50
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1.01
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Delta
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0.47
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0.17
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Gamma
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0.045
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0.026
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Vega
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0.08
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0.06
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A spreader expects volatility to decline and is willing to set up a position where
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by he will profit by $250 for each one percentage decrease in volatility. Moreover, he
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wants to be gamma and delta neutral. He knows that he can eventually neutralize any
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delta by using XYZ common stock, as in the previous example. How many options
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should be spread to achieve the desired result? |