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Rho

In short

Sensitivity to interest rate changes — least impactful of the main Greeks

Rho measures how much an option's price changes when interest rates change. It's the least important Greek for short-term options but matters for long-dated LEAPS. Rising rates benefit calls and hurt puts.

Rho measures the sensitivity of option price to a 1% change in the risk-free interest rate. Call options have positive rho; puts have negative rho. Most traders focus on delta, gamma, theta, and vega — rho matters mainly for long-dated options (1+ year).

Formula

Rho = ∂Option Price ÷ ∂Risk-Free Rate

Related concepts

  • Delta — If a call has delta of 0.5, it gains $0.50 for every $1 the stock rises. Delta 1.0 means the option moves dollar-for-dollar with the stock. At-the-money options typically have delta near 0.5.
  • Vega — Vega measures how much an option's price changes when market expectations of volatility change. If you expect a big announcement (earnings, FDA), buy before the event — vega will boost your option's value as uncertainty rises.
  • Risk-Free Rate — The rate you earn on the safest available investment, typically short- to medium-term government debt. Everything else gets compared against it — if a 10-year government bond pays 4%, why accept only 3% from a riskier stock or corporate bond with no extra compensation?
  • Expiration Date — Options have a use-by date. After expiration, they're worthless unless exercised. Shorter expirations are cheaper but give you less time to be right. Longer expirations (LEAPS) cost more but give the trade more time to work.