Synthetics (Continued)
A short (negative) put is equal to a short (negative) call plus long stock, after the basis adjustment. Consider that if the put is sold instead of buying stock and selling a call, the interest that would otherwise be paid on the cost of the stock up to the strike price is a savings to the put seller. To balance the equation, the interest benefit of the short put must be added to the call side (or subtracted from the put side). It is the same with dividends.
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The dividend benefit of owning the stock must be subtracted from the call side to make it equal to the short put side (or added to the put side to make it equal the call side). The same delta concept applies here. The short 50-strike put in our example would have a 0.45 delta. The short call would have a –0.55 delta. Buying one hundred shares along with selling the call gives the synthetic short put a net delta of 0.45 (–0.55 plus 1.00).
Short Call Versus Short Put + Short Stock
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Similarly, a synthetic short call can be created by selling a put and selling (short) one hundred shares of stock. FIGURE 6.4 shows a conceptual overview of these two positions at expiration. Put/call parity can be manipulated as shown here to illustrate the composition of the synthetic short call.
- –Call = –Put –Stock + Strike –Interest + Dividend
Most professional traders earn a short stock rebate on the proceeds they receive when they short stock—an advantage to the short-put + short-stock side of the equation. Additionally, short-stock sellers must pay dividends on the shares they are short—a liability to the married-put seller. To make all things equal, one subtracts interest and adds dividends to the put side of the equation.
Comparing Synthetic Calls and Puts
The common thread among the synthetic positions explained above is that, for a put-call pair, long options have synthetic equivalents involving long options, and short options have synthetic equivalents involving short options. After accounting for the basis, the four basic synthetic option positions are:
- Long Call = Long Put + Long Stock
- Short Call = Short Put + Short Stock
- Long Put = Long Call + Short Stock
- Short Put = Short Call + Long Stock
Because a call or put position is interchangeable with its synthetic position, an efficient market will ensure that the implied volatility is closely related for both. For example, if a long call has an IV of 25%, the corresponding put should have an IV of about 25%, because the long put can easily be converted to a synthetic long call and vice versa.
The “Greeks” will be similar for synthetically identical positions, too. The long options and their synthetic equivalents will have positive gamma and vega with negative theta. The short options and their synthetics will have negative gamma and vega with positive theta.
This article series concludes with Part 4 tomorrow.
| Read Part 1 | Read Part 2 |
By Dan Passarelli of Market Taker Mentoring, LLC
