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