28 lines
1.7 KiB
Plaintext
28 lines
1.7 KiB
Plaintext
to offsetting each other. For all intents and purposes, the trader is out of the
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primary risks of the position as measured by greeks when a position is
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converted. Let’s look at a more detailed example.
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A trader executes the following trade (for the purposes of this example,
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we assume the stock pays no dividend and the trade is executed at fair
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value):
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Sell one 71-day 50 call at 3.50
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Buy one 71-day 50 put at 1.50
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Buy 100 shares at $51.54
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The trader buys the stock at $51.54 and synthetically sells the stock at
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$52. The synthetic price is computed as −3.50 + 1.50 − 50. Therefore, the
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stock is sold synthetically at $0.46 over the actual stock price.
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Exhibit 6.8 shows the analytics for the conversion.
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EXHIBIT 6.8 Conversion greeks.
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This position has very subtle sensitivity to the greeks. The net delta for
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the spread has a very slightly negative bias. The bias is so small it is
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negligible to most traders, except professionals trading very large positions.
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Why does this negative delta bias exist? Mathematically, the synthetic’s
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delta can be higher with American options than with their European
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counterparts because of the possibility of early exercise of the put. This
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anomaly becomes more tangible when we consider the unique directional
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risk associated with this trade.
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In this example, the stock is synthetically sold at $0.46 over the price at
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which the stock is bought. If the stock declines significantly in value before
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expiration, the put will, at some point, trade at parity while the call loses all
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its time value. In this scenario, the value of the synthetic stock will be short
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at effectively the same price as the actual stock price. For example, if the
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stock declines to $35 per share then the numbers are as follows: |