Since we are perhaps on the verge of interest rates actually not being zero, I thought a quick review of the least known “Greek”, RHO, would be in order. 

The RHO of an option is the change in option value that results from a change in interest rates. The theoretical value changes in relation to a one- percentage-point movement in the underlying interest rate.

For example, say the theoretical price of a call option is $8.25 and the Rho value is .25. If interest rates increase from 2% to 3% then the price of that option will theoretically increase to $8.50. Conversely, if interest rates decrease from 3% to 2%, the price of that call option will theoretically decrease to $8.00.

Rho is greatest for options that are in-the-money and decreases rapidly as the option moves out-of-the-money. Rho is also greater in options with greater time to expiration. You can understand this by thinking about the effect that interest rates have on the cost of carry on an option:

In-the-money options and options with a longer time to expiration have higher premiums and therefore require more cash to hold the option all the way until the expiration date.

Note that interest rates affect call and put options in an opposite manner. When interest rates rise, the value of call options increase and the value of put options decrease. When interest rates fall, the value of call options decrease and the value of put options increase.

Here is a quick summary to help clarify things:

  • Stock options are actually substitutes for buying or selling actual stock.
  • If you use your cash to buy stock, then your money is no longer earning interest in your bank account.
  • If you control the same amount of stock using options, and thus invest using much less cash, the remaining cash will earn interest.
  • If interest rates rise, there is more incentive to keep cash in the bank account, so call options become more attractive than buying stock.
  • More attractive means more demand, therefore price increases.
  • On the contrary, if you sell stock you collect money and deposit the cash in your bank account, thus earning interest.
  • Put options are alternatives to selling stock. This removes the benefit of having the extra money in your bank account.
  • So when rates are increasing, interest in put options decreases because investors would rather sell the actual stock.
  • Less attractive means less demand, therefore price decreases.