37 lines
2.8 KiB
Plaintext
37 lines
2.8 KiB
Plaintext
Chapter 40: Advanced Concepts 885
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Note: All the equations cannot be set equal to zero, or the solution will be all
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zeros. This is easily handled by setting at least one equation equal to a small, nonzero
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quantity, such as 0.1. As long as at least one of the risk factors is nonzero, one can
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determine the neutral ratio for all other factors merely by solving these simultaneous
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equations. There are plenty of low-cost computer programs that can solve simultane
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ous equations such as these.
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This concept can be carried to greater lengths in order to determine the best
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spread to create in order to achieve the desired results. One might even try to use
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three different options, using the third option to neutralize delta, so that he wouldn't
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have to neutralize with stock. The third equation would use deltas as constants and
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would be set to equal zero, representing delta neutral. Solving this would require
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solving three equations in three unknowns, a simple matter for a computer.
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As long as at least one of the risk factors is nonzero, one can determine the neu
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tral ratio for all other factors merely by solving these simultaneous equations. Even
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more importantly, the computer can scan many combinations of options that produce
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a position that is both gamma and delta neutral and has a specific position vega
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(-$238, for example). One would then choose the "best" spread of the available pos
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sibilities by logical methods including, if possible, choosing one with positive theta,
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so time is working in his favor.
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To summarize, one can neutralize all variables, or he can specify the risk that he
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wants to accept in any of them. Merely write the equations and solve them. It is best
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to use a computer to do this, but the fact that it can be done adds an entirely new,
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broad dimension to option spreading and risk-reducing strategies.
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EVALUATING A POSITION USING THE RISK MEASURES
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The previous sections have dealt with establishing a new position and determining its
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neutrality or lack thereof. However, the most important use of these risk measures is
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to predict how a position will perform into the future. At a minimum, a serious strate
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gist should use a computer to print out a projection of the profits and losses and posi
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tion risk at future expected prices. Moreover, this type of analysis should be done for
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several future times in order to give the strategist an idea of how the passage of time
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and the resultant larger movements by the underlying security would affect the posi
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tion.
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First, one would choose an appropriate time period - say, 7 days hence - for the
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first analysis. Then he should use the statistical projection of stock prices (see Chapter
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28 on mathematical applications) to determine probable prices for the underlying
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security at that time. Obviously, this stock price projection needs to use volatility, and |