Rho

Rho is an estimate of how much the theoretical value of an option changes when interest rates move 1.00%. The rho for a call and put at the same strike price and the same expiration month are not equal. Rho is one of the least used greeks. When interest rates in an economy are relatively stable, the chance that the value of an option position will change dramatically because of a drop or rise in interest rates is pretty low. Nevertheless, we’ll describe it here for your edification.

Long calls and short puts have positive rho. Short calls and long puts have negative rho. How does this happen? The cost to hold a stock position is built into the value of an option. It all has to do with the idea of an option being a substitute of sorts for a stock position. For example, if you think the stock of XYZ is going to rise, you could buy 100 shares of XYZ for $4800, or you could buy 2 of the XYZ Aug 50 calls for $400. (2 XYZ Aug 50 calls would give me a position delta of +90 — pretty close to the XYZ stock position delta of +100.) As you can see, you would have to spend about 12X the amount spent on the options that you would spend on the stock. That means that you would have to borrow money or take cash out of an interest-bearing account to buy the stock. That interest cost is built into the call option’s value.

The more expensive it is to hold a stock position, the more expensive the call option. An increase in interest rates increases the value of calls and decreases the value of puts. A decrease in interest rates decreases the value of calls and increases the value of puts.

Back to the XYZ Aug 50 calls. They have a value of $2.00 and a rho of +.02 with XYZ at $48.00 and interest rates at 5.00%. If interest rates increase to 6.00%, the value of the XYZ Aug 50 calls would increase to $2.02. If interest rates decrease to 4.00%, the value of the XYZ Aug 50 calls would decrease to $1.98.