Option Theta Calculator
Estimate an option’s theta — the daily time decay of its premium — for a call or put using Black–Scholes, in both per-day and annual terms.
How it works
Theta_call = −(S·φ(d1)·σ)/(2√T) − rK·e^(−rT)·N(d2) · Theta_put = −(S·φ(d1)·σ)/(2√T) + rK·e^(−rT)·N(−d2) · per day = Theta ÷ 365
Theta measures how much an option loses simply because a day has passed, holding spot and volatility fixed. It comes almost entirely from the erosion of time value, so it is largest for at-the-money options and accelerates as expiry nears. Option sellers collect theta while buyers pay it — which is why short-dated at-the-money options bleed fastest.
Worked example
For a $100 at-the-money call with 25% vol, a 4% rate and three months (T = 0.25) to expiry, φ(d1) ≈ 0.39, so the annual theta is roughly −$10 and the daily theta about −$0.028 per share, or −$2.80 per contract each day.
Sources: Greeks (finance) — Wikipedia
Frequently asked questions
Why divide annual theta by 365 and not 252?
Time decay happens on calendar days, including weekends, so options lose value over the weekend too. Dividing by 365 gives the average calendar-day decay; some traders use 252 trading days when they want a per-trading-day figure.
Is theta always negative for a buyer?
For long options, essentially yes — time decay works against you. Deep in-the-money European puts can show tiny positive theta because of the discounting term, but for practical long positions theta is a cost.
When is theta the most punishing?
For at-the-money options in the final weeks before expiry. The time-value curve steepens sharply near expiry, so a position that decayed slowly for months can lose value rapidly in the last stretch.
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Educational estimate using a simplified Black–Scholes / options model — no dividends, no early-exercise, no fees or slippage. Options are high-risk. Not investment advice.