Synthetic Put and Call Spreads Made Easy (Part 4)
09/04/2009 12:01 am EST
Put/call parity was designed for European-style options. The early exercise possibility of American-style options gums up the works a bit. Because a call (put) and a synthetic call (put) are functionally the same, it is logical to assume that the implied volatility and the Greeks for both will be the same, too. This is not necessarily true with American-style options.
However, put/call parity may still be useful with American options when the limitations of the equation are understood. With at-the-money, American-exercise options, the differences in the Greeks for a put/call pair are subtle. FIGURE 6.5 is a comparison of the Greeks for the 50 strike call and the 50 strike put with the underlying at $50 and 66 days until expiration.
Figure 5: Greeks for a 50 Strike Put/Call Pair on a $50 Stock
The examples used earlier in this article to describe the deltas of synthetics were predicated on the rule of thumb that the absolute values of call and put deltas add up to 1.00. To be a bit more realistic, consider that because of American exercise, the absolute delta values of put/call pairs don’t always add up to 1.00.
In fact, Figure 5 shows that the call has closer to a –.554 delta. The put struck at the same price, and then has a .457 delta. By selling 100 shares against the long call, we can create a combined position delta (call delta plus stock delta) that is very close to the put’s delta. The delta of this synthetic put is –0.446 (0.554 minus 1.00). The delta of a put will always be similar to the delta of its corresponding synthetic put. This is also true with call/synthetic call deltas. This relationship, mathematically, is:
This holds true whether the options are in-, at-, or out-of-the-money. For example, with a stock at $54, the 50 put would have a –.205 delta and the call would have a .799 delta. Selling 100 shares against the call to create the synthetic put yields a net delta of –.201.
If long or short stock is added to a call or put to create a synthetic, delta will be the only Greek affected. With that in mind, note the other Greeks displayed in Figure 5—especially theta. Proportionally, the biggest difference in the table is in theta. The disparity is due in part to interest. When the effects of the interest component outweigh the effects of the dividend, the time value of the call can be higher than the time value of the put.
Because the call must lose more premium than the put by expiration, the theta of the call must be higher than the theta of the put. American exercise can also cause the option prices in put/call parity to not add up. Deep in-the-money puts can trade at parity, while the corresponding call still has time value. The put/call equation can be unbalanced. The same applies to calls on dividend-paying stocks as the dividend date approaches. When the date is imminent, calls can trade close to parity, while the puts still have time value. The role of dividends will be discussed in further articles.
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By Dan Passarelli of Market Taker Mentoring, LLC