The r (rho)
How much does the option price change if the risk-free interest rate
is changing by a small amount (e.g. 0.1 %)?
You own a CALL option for one share of some internet stock (prices of internet stock
dependent on interest rates - they have to borrow money all the time).
Right now the interest rate is
4% per year. You look up the value for your
option - it has a value of $3. Assume that just now interest rates
jump by 0.1 % per year to 4.1%
per year -
strike price, stock price stay unchanged (for the moment, later they will adjust, of course).
The value of the option for the new interest rate is $3.10.
The r for the stock option is
the difference in option price:
$3.10 - $3.00 = $0.10
change in interest rate: 4.1% - 4% = 0.1% = 0.1/100 = 0.001
r = $0.10 / 0.001 = 100
Do not forget that this value for r assumes that you state option prices in Dollars and
use annual interest rates (e.g. for semi-annual interest rates the result would be different).
The r tells you by how much the option price changes if
interest rates fluctuate. To understand how r
depends on stock and strike price, volatility and other quantities play around with the
Let us turn to yet another greek ...