36 lines
2.6 KiB
Plaintext
36 lines
2.6 KiB
Plaintext
Chapter 40: Advanced Concepts 881
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Hence, it is always a simple matter to create a position that is both gamma and delta
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neutral. In fact, it is just as simple to create a position that is neutral with respect to
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delta and any other risk measure, because all that is necessary is to create a neutral
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ratio of the other risk measure (gamma, vega, theta, etc.) and then eliminate the
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resulting position delta by using the underlying.
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In theory, one could construct a position that was neutral with respect to all five
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risk measures (or six, if you really want to go overboard and include "gamma of the
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gamma" as well). Of course, there wouldn't be much profit potential in such a posi
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tion, either. But such constructions are actually employed, or at least attempted, by
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traders such as market-makers who try to make their profits from the difference
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between the bid and off er of an option quote, and not from assuming market risk
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Still, the concept of being neutral with respect to more than one risk factor is a
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valid one. In fact, if a strategist can determine what he is really attempting to accom
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plish, he can often negate other factors and construct a position designed to accom
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plish exactly what he wants. Suppose that one thought the implied volatility of a cer
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tain set of options was too high. He could just sell straddles and attempt to capture
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that volatility. However, he is then exposed to movements by the underlying stock He
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would be better served to construct a position with negative vega to reflect his expec
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tation on volatility, but then also have the position be delta neutral and gamma
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neutral, so that there would be little risk to the position from market movements. This
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can normally be done quite easily. An example will demonstrate how.
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Example: XYZ is 48. There are three months to expiration, and the volatility of XYZ
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and its options is 35%. The following information is also known:
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XYZ:48
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Option Price Delta Gamma Vega
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April 50 call 2.50 0.47 0.045 0.08
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April 60 call l.00 0.17 0.026 0.06
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For whatever reasons - perhaps the historical volatility is much lower - the
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strategist decides that he wants to sell volatility. That is, he wants to have a negative
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position vega so that when the volatility decreases, he will make money. This can
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probably be accomplished by buying some April 50 calls and selling more April 60
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calls. However, he does not want any risk of price movement, so some analysis must
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be done.
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First, he should determine a gamma neutral spread. This is done in much the
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same manner as determining a delta neutral spread, except that gamma is used. |