Call Option Theta

Options
Updated Apr 2026 • Has calculator

The daily time decay of a call option's price, holding all other factors constant.

What is Theta (Call)?

Theta (Θ) measures how much a call option loses in value each calendar day as time passes, all else equal. It is almost always negative for long options — the option buyer pays for time value that erodes daily. Theta accelerates as expiration approaches, especially for at-the-money options. A theta of −$0.05 means the call loses $0.05 in value every day, or $5.00 per contract.

Formula

Θ_call = [−S·φ(d₁)·σ / (2√T) − r·K·e^(−rT)·N(d₂)] / 365

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, σ = 28%, T = 0.25 yrs, r = 5.25%
Step 2  Annual theta: −S·φ(d₁)·σ/(2√T) − r·K·e^(−rT)·N(d₂)
Step 3  = −(185×0.393×0.28/1.00) − (0.0525×185×0.987×0.565)
Step 4  = −20.35 − 5.41 = −25.76 per year
Step 5  Θ per day = −25.76 / 365 ≈ −$0.0706 per share per day
Step 6  → This 3-month ATM call loses ~$7.06 per contract per calendar day

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

Calculate Theta (Call)

Current market price of the underlying stock

Option strike price

Annual risk-free rate

Time to expiration in years

Annualised implied volatility

Theta (per day)

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Not investment advice.

How to Interpret Theta (Call)

< -0.1
High decay — short-dated ATM option, sell premium
-0.1 – -0.03
Moderate decay — typical near-term option
-0.03 – -0.01
Low decay — long-dated or far OTM/ITM option
> -0.01
Minimal decay — very long-dated LEAPS or deep ITM

📚 Options Basics — Complete the path

  1. Delta (Call)
  2. Gamma
  3. Theta (Call)
  4. Vega
  5. BS Call
Sources
  1. Hull, J.C. — Options, Futures, and Other Derivatives, 11th ed.
  2. Investopedia — Theta