30 lines
1.7 KiB
Plaintext
30 lines
1.7 KiB
Plaintext
American-Exercise Options
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Put-call parity was designed for European-style options. The early exercise
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possibility of American-style options gums up the works a bit. Because a
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call (put) and a synthetic call (put) are functionally the same, it is logical to
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assume that the implied volatility and the greeks for both will be exactly the
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same. This is not necessarily true with American-style options. However,
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put-call parity may still be useful with American options when the
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limitations of the equation are understood. With at-the-money American-
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exercise options, the differences in the greeks for a put-call pair are subtle.
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Exhibit 6.5 is a comparison of the greeks for the 50-strike call and the 50-
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strike put with the underlying at $50 and 66 days until expiration.
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EXHIBIT 6.5 Greeks for a 50-strike put-call pair on a $50 stock.
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Call Put
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Delta 0.5540.457
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Gamma0.0750.078
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Theta 0.0200.013
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Vega 0.0840.084
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The examples used earlier in this chapter in describing the deltas of
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synthetics were predicated on the rule of thumb that the absolute values of
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call and put deltas add up to 1.00. To be a bit more realistic, consider that
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because of American exercise, the absolute delta values of put-call pairs
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don’t always add up to 1.00. In fact, Exhibit 6.5 shows that the call has
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closer to a 0.554 delta. The put struck at the same price then has a 0.457
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delta. By selling 100 shares against the long call, we can create a combined-
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position delta (call delta plus stock delta) that is very close to the put’s
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delta. The delta of this synthetic put is −0.446 (0.554 − 1.00). The delta of a
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put will always be similar to the delta of its corresponding synthetic put.
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This is also true with call–synthetic-call deltas. This relationship
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mathematically is
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