Rho definition

What is rho in options trading?

Rho is a term used in options trading to refer to how sensitive an option’s price is to any changes in interest rate levels. Rho can be either positive or negative depending on whether the position is long or short, and whether the option is a call or a put.

A positive rho can apply to long call options and short put options because the price of these options is positively correlated with any increases or decreases in interest rates. If rates rise, they will increase in value and if rates are cut, they will fall in value.

On the other hand, a negative rho applies to short calls and long puts because the price of these options is negatively correlated with increases or decreases in interest rates. If rates rise, these options will fall in value, and if rates fall, they will rise.

Options that are at the money with a moderate time to expiry are the most sensitive to interest rate changes. This is because any changes in interest rates could have a significant impact on whether the option expires in the money or out of the money.

Rho calculation

The actual calculation for rho is very complicated, and few traders do it manually. Put simply, rho seeks to establish the sensitivity of an option’s price given a 1% change in the underlying interest rate. So, after a 1% increase or decrease in the underlying interest rate, the price of an options contract would be adjusted according to the rho value.

Rho example

As an example of rho in options trading, let’s assume that interest rates have just increased from 2% to 3%. Now, let’s suppose that a long call option is comfortably in the money with a rho of just 0.02 and a price of £1.20. Given the 1% increase in interest rates, the value of this call option has gone from £1.20 to £1.22, which you’d get by adding the rho of 0.02 to the current market price of £1.20.

On the other hand, if you were dealing long put options and interest rates increased from 2% to 3%, the price of the put would likely decrease. This would be achieved by subtracting the rho value from the current option value after a 1% increase in interest rates. For example, if the rho of a put option was -0.15 and the current value of the put option was £2.00, you would assume that given a 1% increase in interest rates, the value of the put option would fall to £1.85.