Rho is one of the options Greeks and represents the sensitivity of an option's price to changes in the risk-free interest rate (the theoretical return on a riskless investment). It is the partial derivative of the option price with respect to the interest rate, often denoted as ∂Price/∂r. The concept helps describe how economic conditions that affect rates can influence option values.
In practice, rho can indicate how much an option's price might move if interest rates rise or fall. For call options, rho is typically positive (prices tend to rise with higher rates); for put options, rho is typically negative. The magnitude of rho generally grows with longer times to expiration and with certain moneyness conditions that affect the carry and present value aspects of the payoff. Rho is usually smaller in magnitude than other greeks like delta or vega, but it becomes more relevant when rates are expected to move significantly or when options have long horizons.
Rho is a standard input in pricing models such as Black-Scholes and in scenario analyses used for risk management. It also applies to options on futures, though the behavior can differ due to how carry and discounting interact in those models. Like all greeks, rho is an estimate based on model assumptions and current inputs; real-world price changes depend on multiple factors changing simultaneously.
If a European call option on a stock has a rho of 0.25, a 1 percentage-point rise in the risk-free rate would, all else equal, increase the option's price by about 0.25.
Delta · Gamma · Theta · Vega · Black-Scholes model · Interest rate risk