33 lines
2.3 KiB
Plaintext
33 lines
2.3 KiB
Plaintext
or
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With American options, a put this far in-the-money with less than 71 days
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until expiry will be all intrinsic value. Interest, in this case, will not factor
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into the put’s value, because the put can be exercised. By exercising the put,
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both the long stock leg and the long put leg can be closed for even money,
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leaving only the theoretically worthless call. The stock-synthetic spread is
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sold at 0.46 and essentially bought at zero when the put is exercised. If the
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put is exercised before expiration, the profit potential is 0.46 minus the
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interest calculated between the trade date and the day the put is exercised.
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If, however, the conversion is held until expiration, the $0.46 is negated by
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the $0.486 of interest incurred from holding long stock over the entire 71-
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day period, hence the trader’s desire to see the stock decline before
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expiration, and thus the negative bias toward delta.
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This is, incidentally, why the synthetic price (0.46 over the stock price)
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does not exactly equal the calculated value of the interest (0.486). The
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trader can exercise the put early if the stock declines and capitalize on the
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disparity between the interest calculated when the conversion was traded
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and the actual interest calculation given the shorter time frame. The model
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values the synthetic at a little less than the interest value would indicate—in
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this case $0.46 instead of $0.486.
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The gamma of this trade is fairly negligible. The theta is slightly positive.
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Rho is the figure that deserves the most attention. Rho is the change in an
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option’s price given a change in the interest rate.
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The −0.090 rho of the conversion indicates that if the interest rate rises
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one percentage point, the position as a whole loses $0.09. Why? The
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financing of the position gets more expensive as the interest rate rises. The
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trader would have to pay more in interest to carry the long stock. In this
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example, if interest rises by one percentage point, the synthetic stock, which
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had an effective short price of $0.46 over the price of the long stock before
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the interest rate increase, will be $0.55 over the price of the long stock
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afterward. If, however, the interest rate declines by one percentage point,
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the trader profits $0.09, as the synthetic is repriced by the market to $0.37
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over the stock price. The lower the interest rate, the less expensive it is to |