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