  ## OPTIONS  ## Monday, July 2, 2007

### Option Greeks: RHO

Rho is a measure of the change in an option's price due to a change in interest rate. Rho estimates how much the option’s price will change when interest rates changes by 1%.
Rho is seldom used because interest rates are normally pretty stable. Therefore, the chance that option’s price will change drastically due to a rise or a drop in interest rate will be quite low.

Example:
The current price of ABC May 50 Call is \$3 with a Rho of +0.03 and interest rate at 5%.
If interest rates increase to 6%, the value of ABC May 50 Call will increase to \$3.03.
If interest rates decrease to 4%, the value of ABC May 50 Call will decrease to \$2.97.

Rho and the position in the market:
Long calls and short puts have positive rho.
Short calls and long puts have negative rho.

Positive rho means the option price increases when the interest rate increases, and decreases when the interest rate decreases.
Negative rho means the option price decreases when the interest rate increases, and increases when the interest rate decreases.

The impact of interest rate on option’s price has something to do with the “carrying cost” of stocks. When you are bullish on a certain stock, instead of buying the stock, you can alternatively buy Call options, as it is much cheaper to buy Call options than the stock itself. The interest cost should you buy the stocks is built into the Call option’s value.

Example:
ABC stock is now trading at \$49. If you expect ABC stock to increase in the near future, you could buy 100 shares of ABC for \$4,900, or you could buy 2 contracts of ABC May 50 Call (at \$2.9 per contract, with delta of 0.47) for \$580. The 2 contracts of ABC May 50 Call will give you a position delta of +0.94 (=2 x 0.47), close to the ABC stock position delta of +1.
If you buy the stocks, you would have to spend about 8.4 times the amount spent on the options. That means you would have to borrow money or take cash out of your interest-bearing account to buy the stock. That interest cost is built into the Call option’s price. The higher the interest rate, the more expensive it is to hold a stock position, and as a result, the more expensive the Call options would be.

Some characteristics of Rho:

* An increase in interest rates will increase the value of Call options and decrease the value of Put options.
A decrease in interest rates decreases the value of Call options and increases the value of Put options.

* For both Calls & Puts, the longer the time to expiration, the larger is the impact of the interest rate on the option value (i.e. the higher is the rho).

* Deep OTM (Out-of-the-money) options tend to have low rho, whereas ATM (At-the-money) & Deep ITM (In-the-money) options relatively have a higher rho.

To read about other Option Greeks, go to: Option Greeks.

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