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:
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 percent, the
corresponding put should have an IV of about 25 percent, 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.