EXHIBIT 6.2 Long put vs. long call + short stock.
The concept of synthetics can become more approachable when studied
from the perspective of delta as well. Take the 50-strike put and call listed
on a $50 stock. A general rule of thumb in the put-call pair is that the call
delta plus the put delta equals 1.00 when the signs are ignored. If the 50 put
in this example has a −0.45 delta, the 50 call will have a 0.55 delta. By
combining the long call (0.55 delta) with short stock (–1.00 delta), we get a
synthetic long put with a −0.45 delta, just like the actual put. The
directional risk is the same for the synthetic put and the actual put.
A synthetic short put can be created by selling a call of the same month
and strike and buying stock on a share-for-share basis (i.e., a covered call).
This is indicated mathematically by multiplying both sides of the put-call
parity equation by −1:
The at-expiration diagrams, shown in Exhibit 6.3 , are again conceptually
the same.