Rho (ρ) is one of the options greeks which are collectively used to determine how closely an options or warrants contract will track its underlying market. Specifically, rho is the rate at which the value of an options or warrants contract will change in relation to the risk free interest rate (i.e. the rate of return of a risk free trade). Rho is one of the first order derivatives, but is one of the least used options greeks.
Calculation
Rho (ρ) is the first derivative of the value (V) of an options or warrants contract, with respect to the risk free interest rate (r). Rho is calculated as shown in the above calculation image.
Use In Trading
Rho (ρ) is the number of points that the value of an options or warrants contract will increase or decrease as the risk free interest rate increases or decreases by 1%. Rho can be either a positive or negative number depending upon the direction that the value will move compared to the direction of the change in the risk free interest rate. For example, the price of a long call with a rho of 12.25 will increase by $12.25 (or € or £, etc.) for every increase of 1% in the risk free interest rate (i.e. the rate of return of a free risk trade).
