19 lines
1.0 KiB
Plaintext
19 lines
1.0 KiB
Plaintext
Rho and Time
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The time component of interest has a big impact on the magnitude of an
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option’s rho, because the greater the number of days until expiration, the
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greater the interest. Long-term options will be more sensitive to changes in
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the interest rate and, therefore, have a higher rho.
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Take a stock trading at about $120 per share. The July, October, and
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January ATM calls have the following rhos with the interest rate at 5.5
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percent.
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Option Rho
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July (38-day) 120 calls+0.068
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October (130-day) 120 calls+0.226
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January (221-day) 120 calls+0.385
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If interest rates rise 25 basis points, or a quarter of a percentage point, the
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July calls with only 38 days until expiration will gain very little: only
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$0.017 (0.068 × 0.25). The October 120 calls with 130 days until expiration
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gain more: $0.057 (0.226 × 0.25). The January calls that have 221 days
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until they expire make $0.096 theoretically (0.385 × 0.25). If all else is held
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constant, the more time to expiration, the higher the option’s rho, and
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therefore, the more interest will affect the option’s value. |