About Rho

Rho

Rho, is the least mentioned among the greeks; delta, gamma, theta and vega.

Rho measures the impact the change in 1% risk free interest rate has on the value of the option.

In a gist, when Rho increases, the values of all Call options will increase and the values of all Put options will decrease.This occurs to every strike and expiration month options For example,

CSX : $61.61
35day 60Call : 5.10
35day 60Put : 3.40

The current risk free IR is 2%. Suppose, we increase that risk free IR by 1% to 3%, the revised Call and Put values will change. This change is caused by Rho.

35day 60Call : 5.13 (increased from 5.10)
35day 60Put : 3.37 (decreased from 3.37)

Explanation:

The reason that Calls become more expensive when IR increases, is because of "cost of carry". Remember that Call buyers have the right to exercise their Call options at any time before expiration. Supposing a trader had Long +10 6-month 55Call and is now ITM.
He could exercise this 55Call option and take delivery of CSX at $55/share but he will have to fork out $55,000 for this transaction immediately. He will still have the right to exercise his ITM Call option the next day, next week, next month or even right at the end of that 60day period. Why exercise it now, fork out $55,000 when he can deploy his $55,000 into a risk free instrument and obtain an assured interests for the next 6 months?
Of cos, if he feels that CSX will not rally any further from that juncture, he would be better just to close off this 55Call, take his profit and move on.
Hence, when risk free IR goes up, the less motivated a ITM Call option holder will be to exercise his call option. Since more people will be unwilling to do so when IR goes up, this premium is then reflected in the call option value. This is called the Cost of Carry.

Conversely, if a trader had a 60day ITM Put option, eg 60day 90Put, he will have the right to sell CSX at that strike price. Better for the trader to sell CSX at $90/share, quickly take his cash and put into a risk free instrument and earn the increased interests when holding onto those Put options earns no interest whatsoever. Hence, when Rho increases, more Put option holders will exercise their Put. Put values will drop as a consequence of increased Rho.

It would have to take a huge and sudden movement in risk free IR to have any significant impact on option values. And when such IR changes drastically, we have bigger issues to worry about.
Afterall, should the Fed Reserve Bank, decide tomorrow to raise IR from 2% to 5%, i doubt you will be rushing out to buy Call options, even when theoretically, the call values will rise.

Rho is primarily used by market makers when they hedge their positions against clients' and to price option premiums. Since they normally have very large, complex and constantly changing positions, they will take advantage of Rho to the maximum. Not so applicable for retail traders.

It is for completeness of Greek discussion, that I briefly elaborate on Rho.