44 lines
2.1 KiB
Plaintext
44 lines
2.1 KiB
Plaintext
630 Part V: Index Options and Futures
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be interested in neutrality. The key to determining one's neutrality, of course, is tc
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use the delta of the option. In the case of the PERCS stock, one would have to usE
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the delta of the imbedded call.
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Example: An investor is long 1,000 shares ofXYZ PERCS maturing in two years. He
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thinks XYZ is stuck in a trading range and does not expect much volatility in the near
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future. Thus, a ratio write appeals to him. How many calls should he sell in order to
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create a neutral position against his 1,000 shares?
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First, he needs to compute the delta of the imbedded option in the PER CS, and
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therefore the delta of the PERCS itself. The delta of a PERCS is not 1.00, as is the
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delta of common stock.
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Assume the XYZ PERCS matures in two years. It is redeemable at 39 at that
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time. XYZ common is currently trading at 33. The delta of a two-year call with strik
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ing price 39 and common stock at 33 can be calculated (the dividends, short-term
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interest rate, and volatility all play a part). Suppose that the delta of such an option is
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0.30. Then the delta of the PER CS can be computed:
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PERCS delta= 1.00- Delta of imbedded call
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= 1.00 - 0.30 = 0.70 in this example
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Assume the following data is known:
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Security
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XYZ Common
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XYZ PERCS
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XYZ October 40 call
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Price
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33
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34
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2
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Delta
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1.00
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0.70(!)
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0.35
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Being long 1,000 PER CS shares is the equivalent of being long 700 shares of
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common (ESP= 1,000 x 0.70 = 700). In order to properly hedge that ESP with the
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October 40 call, one would need to sell 20 October 40 calls.
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Quantity to sell = ESP of PER CS/ESP of October 40 call
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= 700/(100 shares per option x 0.35)
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= 700/35 = 20
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Thus, the position - long 1,000 PER CS, short 20 October 40 calls - is a neutral one
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and it is a ratio write.
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One may not want to have such a steep ratio, since the result of this example is
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the equivalent of being long 1,000 common and short 30 calls in total (10 are imbed
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ded in the long PERCS). Consequently, he could look at other options - perhaps
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writing in-the-money October calls - that have higher deltas and won't require so
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many to be sold in order to produce a neutral position. |