The Effect of Time on Rho
The more time until expiration, the greater the effect interest rate changes
will have on options. In the previous example, a 25-basis-point change in
the interest rate on the 80-strike based on a three-month period caused a
change of 0.05 to the interest component of put-call parity. That is, 80 ×
0.0025 × (90/360) = 0.05. If a longer period were used in the example—say,
one year—the effect would be more profound; it will be $0.20: 80 × 0.0025
× (360/360) = 0.20. This concept is evident when the rhos of options with
different times to expiration are studied.
Exhibit 2.16 shows the rhos of ATM Procter & Gamble Co. (PG) calls
with various expiration months. The 750-day Long-Term Equity
AnticiPation Securities (LEAPS) have a rho of 0.858. As the number of
days until expiration decreases, rho decreases. The 22-day calls have a rho
of only 0.015. Rho is usually a fairly insignificant factor in the value of
short-term options, but it can come into play much more with long-term
option strategies involving LEAPS.
EXHIBIT 2.16 The effect of time on rho (Procter & Gamble @ $64.34)