Options Time Decay Visualizer
Model one European call or put under fixed inputs. Compare remaining calendar days and strike prices; these curves are scenarios, not forecasts.
Read theta as a sensitivity
Theta is the model price change as calendar time passes with other inputs fixed. This page uses European Black–Scholes pricing, constant volatility and interest rate, no dividends, and 365 calendar days per year. It has no quote feed, American early-exercise calculation, transaction costs or multi-leg position aggregation.
Use the curves and comparison view
- Enter positive spot, strike and IV, a finite annual rate, and an integer DTE from 1 to 3650. Blank or invalid fields clear the results.
- Read the single curve from the entered DTE toward zero. At zero DTE, model price equals intrinsic value and extrinsic value is zero.
- Compare all selected DTEs and valid strikes five dollars either side of the entered strike. Moneyness labels use spot and option type; a higher strike is ITM for a put and OTM for a call.
Understand signed extrinsic value
Extrinsic here means European model price minus immediate intrinsic value. It can be negative for some inputs, especially deep ITM puts with positive rates. Clipping it to zero would conceal a consequence of the no-early-exercise assumption. The erosion ratio is −daily theta / positive extrinsic × 100; it is unavailable with a nonpositive denominator. It is not a daily return.
There is no universal acceleration zone
Near-the-money examples can show increasingly negative theta as expiry approaches. Far OTM options can instead approach zero theta, and some ITM European puts have positive theta. The curve is not universally exponential, and 30 or 45 days is not an optimal trading threshold. Changing spot or IV can outweigh the passage of time.
Different starting DTE scenarios with identical strike and other inputs overlap at the same remaining DTE. This is expected from the model, not evidence that their current premiums are equal. Each scenario is one long option; this page does not calculate a spread’s net theta or recommend a position.
References: OIC theta explanation and OIC pricing-model limits.
Frequently Asked Questions
Does theta always become more negative near expiry?
No. At-the-money options can show a steepening curve under fixed inputs, while far out-of-the-money theta can approach zero. Deep in-the-money European puts can have positive theta. There is no universal 30-day boundary or guaranteed daily loss.
What model and units does this page use?
Black–Scholes European call or put pricing with a zero dividend yield, constant spot, IV and rate, and calendar days divided by 365. Prices and theta are per share, not per 100-share contract. Early exercise, fees, spreads and changing market inputs are not modeled.
Why can extrinsic value be negative?
The displayed quantity is model price minus immediate intrinsic value without clipping. A European option cannot be exercised early; discounting can put a deep in-the-money European put below immediate intrinsic value. This is not a model for an American exercise right.
What does the erosion ratio mean?
It is negative daily theta divided by positive extrinsic value, multiplied by 100. A negative ratio means positive theta. It is unavailable when extrinsic value is nonpositive and is an instantaneous sensitivity, not a forecast one-day return or a trading signal.
Why do some comparison curves overlap?
With the same strike and fixed spot, IV and rate, different starting expirations have the same model value at the same remaining DTE. The chart shows each selected DTE plus valid strikes five dollars below and above the entered strike; these are separate single-option scenarios, not a combined spread.
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