Rho and Interest Rates
Rho is a measurement of the sensitivity of an option’s value to a change in
the interest rate. To understand how and why the interest rate is important to
the value of an option, recall the formula for put-call parity stated in
Chapter 6.
Call + Strike − Interest = Put + Stock 1
From this formula, it’s clear that as the interest rate rises, put prices must
fall and call prices must rise to keep put-call parity balanced. With a little
algebra, the equation can be restated to better illustrate this concept:
and
If interest rates fall,
and
Rho helps quantify this relationship. Calls have positive rho, and puts
have negative rho. For example, a call with a rho of +0.08 will gain $0.08
with each one-percentage-point rise in interest rates and fall $0.08 with
each one-percentage-point fall in interest rates. A put with a rho of −0.08
will lose $0.08 with each one-point rise and gain $0.08 in value with a one-
point fall.
The effect of changes in the interest variable of put-call parity on call and
put values is contingent on three factors: the strike price, the interest rate,
and the number of days until expiration.
Interest = Strike×Interest Rate×(Days to Expiration/365) 2
Interest, for our purposes, is a function of the strike price. The higher the
strike price, the greater the interest and, consequently the more changes in
the interest rate will affect the option. The higher the interest rate is, the
higher the interest variable will be. Likewise, the more time to expiration,