Call Option Rho

Options
Updated Apr 2026 • Has calculator

The change in a call option's price for a 1% increase in the risk-free interest rate.

What is Rho (Call)?

Rho (ρ) measures how much a call option's price changes when the risk-free interest rate rises by 1 percentage point. Call rho is always positive: higher rates reduce the present value of the strike payment, making the call more valuable. Rho is largest for deep in-the-money calls and long-dated options. It is the least significant Greek for short-term options but matters for LEAPS and rate-sensitive strategies.

Formula

ρ_call = K · T · e^(−rT) · N(d₂) / 100

Worked Example

Worked example — Apple Inc. (AAPL) — ATM call, representative Q1 2024

Representative Q1 2024 market conditions

Step 1  Stock price (S): $185, Strike (K): $185, r = 5.25%, T = 0.25 yrs, σ = 28%
Step 2  d₂ = 0.083, N(0.083) ≈ 0.533
Step 3  ρ_call = 185 × 0.25 × e^(−0.013) × 0.533 / 100
Step 4  ρ_call = 185 × 0.25 × 0.987 × 0.533 / 100 ≈ $0.243 per share
Step 5  → If the Fed raises rates by 1%, this call gains $0.24 per share ($24 per contract)

Source: Hull, J.C. — Options, Futures, and Other Derivatives, 11th ed., Ch. 19 (2024-01-15)

Calculate Rho (Call)

Current market price of the underlying stock

Option strike price

Annual risk-free rate

Time to expiration in years

Annualised implied volatility

Rho (per 1% rate)

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Not investment advice.

How to Interpret Rho (Call)

< 0.1
Low rho — short-dated option, rate-insensitive
0.1 – 0.5
Moderate rho — intermediate-term call option
0.5 – 1
High rho — long-dated or deep ITM call (LEAPS)
> 1
Very high rho — multi-year deep ITM LEAPS call

📚 Advanced Options — Complete the path

  1. Implied Vol (IV)
  2. Put-Call Parity
  3. Time Value
  4. Rho (Call)
  5. BS Put
Sources
  1. Hull, J.C. — Options, Futures, and Other Derivatives, 11th ed.
  2. Investopedia — Rho