37 lines
2.8 KiB
Plaintext
37 lines
2.8 KiB
Plaintext
Chapter 28: Mathematical Applications 483
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more than fractionally, he may have to add more calls or buy some in, to maintain a
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neutral hedge ratio. This would expose him to some risk, but the risk is substantially
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smaller than if he had not hedged at all. Of course, there would also be certain cases
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in which he would profit by the stock price change. For example, implied volatility
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could decrease, making the calls cheaper.
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A similar hedge can be established by the block trader who sells stock to accom
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modate a customer buy order. He could buy calls in accordance with the hedge ratio,
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to set up a neutral position.
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This process off acilitation is quite widely practiced, especially by brokerage
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houses that are trying to attract the business of the large institutional customer. Since
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the introduction of listed call options and their applications for facilitating orders,
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many quotes for large blocks of stock have improved considerably. The block trader
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(who works for the brokerage house) is willing to make a higher bid or a lower offer
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if he can use options to hedge his position. This facilitation with options results in a
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better market (higher bid or lower off er) from the point of view of the institutional
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customer. Without the availability of such listed options, the block trader would prob
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ably make a bid or an offer that was substantially away from the prevailing market
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price in order to work out of his stock-only position with a lessened degree of risk
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This would obviously present a poorer market for the institutional customer.
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THE NEUTRAL SPREAD
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The hedge ratios of two or more options may be used to determine a neutral spread.
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This strategy is especially useful to market-makers on the options exchanges who may
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want to reduce the risk of options bought or sold in the process of providing a pub
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lic market. If the hedge ratios of two options are known, the neutral ratio is deter
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mined by dividing the two hedge ratios.
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Example: An XYZ January 35 has a hedge ratio of .25, and an XYZ January 30 has a
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hedge ratio of .50, so a neutral ratio would be 2:1 (.50 divided by .25). That is, one
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would sell 2 January 35's against one long January 30, or, conversely, would buy 2
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January 35's against one short January 30. Thus, a market-maker who has just bought
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50 January 30's in an effort to provide a market for a public seller of that call could
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hedge his position by selling 100 January 35's. This should keep his risk small, for
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small stock price changes, until he can unwind the position. The ratio for the neutral
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spread is not as sensitive to the volatility estimate of the underlying stock as is the
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ratio concerning stock and options. This is because the same volatility estimate is
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applied to both options, and the resultant ratio for the spread would not tend to
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change greatly. |