The r   (rho)              

r

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 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 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 OPTIONATOR!.

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