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training_data/curated/text/899df1771bdc8dfbf6f3529c3c18012c51e102a946d5ea9115ff9bb860d96f17.txt

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+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