Put-call parity also aids in valuing options. If put-call parity shows a
difference in the value of the call versus the value of the put with the same
strike, there may be an arbitrage opportunity. That translates as “riskless
profit.” Buying the call and selling it synthetically (short put and short
stock) could allow a profit to be locked in if the prices are disparate.
Arbitrageurs tend to hold synthetic put and call prices pretty close together.
Generally, only professional traders can capture these types of profit
opportunities, by trading big enough positions to make very small profits (a
penny or less per contract sometimes) matter. Retail traders may be able to
take advantage of a disparity in put and call values to some extent, however,
by buying or selling the synthetic as a substitute for the actual option if the
position can be established at a better price synthetically.
Another reason that a working knowledge of put-call parity is essential is
that it helps attain a better understanding of how changes in the interest rate
affect option values. The greek rho measures this change. Rho is the rate of
change in an option’s value relative to a change in the interest rate.
Although some modeling programs may display this number differently,
most display a rho for the call and a rho for the put, both illustrating the
sensitivity to a one-percentage-point change in the interest rate. When the
interest rate rises by one percentage point, the value of the call increases by
the amount of its rho and the put decreases by the amount of its rho.
Likewise, when the interest rate decrease by one percentage point, the value
of the call decreases by its rho and the put increases by its rho. For example,
a call with a rho of 0.12 will increase $0.12 in value if the interest rate used
in the model is increased by one percentage point. Of course, interest rates
usually don’t rise or fall one percentage point in one day. More commonly,
rates will have incremental changes of 25 basis points. That means a call
with a 0.12 rho will theoretically gain $0.03 given an increase of 0.25
percentage points.
Mathematically, this change in option value as a product of a change in
the interest rate makes sense when looking at the formula for put-call parity.
and