Call Theta
Rate of change of call price with respect to the passage of time, expressed per year. Almost always negative — calls lose value as time passes (time decay).
When to use: Use to size time-decay exposure on long or short call positions. Convert to a per-day figure by dividing by 365 (or 252 for trading-day-based brokers) — the "$/day" decay most platforms display.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| Theta | Theta | Change in option price per year of time decay (annualized) | $ |
| S | Stock Price | Current price of the underlying | $ |
| Strike | Strike Price | Exercise price of the option contract | $ |
| Rf | Risk-Free Rate | Continuously compounded annual risk-free rate as a decimal | % |
| Sigma | Volatility | Annualized volatility of the underlying as a decimal (e.g. 0.25 for 25%) | % |
| T | Time to Expiration | Time to expiration in years (e.g. 0.25 for 3 months) | years |
Real-Life Examples
Example 1: ATM Call Theta, 30% Vol, 90 Days
Stock at $100, $100-strike 90-day call, r = 4%, σ = 30%.
Given
Step-by-Step
The call loses about $13.82 per year of time, or roughly $0.038 per calendar day. Theta accelerates as expiration nears — the per-day decay grows even though the per-year figure shrinks.
Frequently Asked Questions
Because all Black-Scholes quantities use annualized inputs (σ, r, T in years). Many broker platforms display theta divided by 365 — the per-calendar-day decay. Convert by dividing this output by 365 (or 252 for trading-day convention).
Rarely, for deep ITM European puts on non-dividend-paying stock when the rate effect dominates: r·K·e^(−rT)·N(−d2) can exceed the volatility-decay term. American puts are exercised early in this regime, eliminating the anomaly.
For ATM options, yes — the per-day decay accelerates roughly as 1/√T, so the last 30 days of an option's life see disproportionately more decay than earlier periods. ITM and OTM options decay more linearly.