The r (rho)
r


How much does the option price change if the riskfree 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
are very
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
divided by
the
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 semiannual 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
OPTIONATOR!.
Let us turn to yet another greek ...
