Calculator Inputs
Formula Used
This calculator uses the Black-Scholes framework for European-style options with continuous dividend yield. Time decay is measured through theta and by repricing the option after time passes.
| d1 | d1 = [ln(S / K) + (r - q + 0.5σ²)T] / [σ√T] |
|---|---|
| d2 | d2 = d1 - σ√T |
| Call Price | C = Se-qTN(d1) - Ke-rTN(d2) |
| Put Price | P = Ke-rTN(-d2) - Se-qTN(-d1) |
| Call Theta | θ = -[Se-qTN'(d1)σ / 2√T] - rKe-rTN(d2) + qSe-qTN(d1) |
| Put Theta | θ = -[Se-qTN'(d1)σ / 2√T] + rKe-rTN(-d2) - qSe-qTN(-d1) |
| Premium Decay | Premium Decay = Current Premium - Premium After Selected Days |
| Extrinsic Decay | Extrinsic Decay = Current Extrinsic Value - Future Extrinsic Value |
Where S is spot price, K is strike price, r is risk-free rate, q is dividend yield, σ is volatility, T is time in years, and N is the standard normal cumulative function.
How to Use This Calculator
- Choose call or put, then choose long or short position.
- Enter spot price, strike price, implied volatility, rate, and dividend yield.
- Set days remaining until expiry and the number of days to move forward.
- Enter contract count and multiplier for position-level results.
- Pick 365 days for calendar basis or 252 for trading-day basis.
- Press the calculate button to show results above the form.
- Review premium decay, theta, extrinsic value, and the time-decay chart.
- Use the export buttons to save a CSV file or a PDF summary.
Example Data Table
| Scenario | Type | Spot | Strike | Volatility | Rate | Dividend | Days | Step | Premium Now | Premium Later | Decay |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Example A | Call | 100.00 | 105.00 | 28.00% | 5.00% | 1.00% | 45 | 7 | 2.15 | 1.82 | 0.33 |
| Example B | Put | 98.00 | 100.00 | 24.00% | 4.00% | 0.00% | 30 | 5 | 3.12 | 2.86 | 0.26 |
| Example C | Call | 120.00 | 115.00 | 18.00% | 3.50% | 0.50% | 20 | 4 | 6.41 | 5.98 | 0.43 |
Frequently Asked Questions
1) What does option time decay mean?
Option time decay is the reduction in an option’s value as expiry approaches, assuming other inputs stay unchanged. It mainly affects extrinsic value.
2) What is theta in options?
Theta measures how much option premium changes for a small reduction in time. It is often quoted per year, then converted to a daily estimate.
3) Why do short options often benefit from time decay?
A short option position generally gains when premium falls. Since time passing often lowers extrinsic value, decay can work in favor of option sellers.
4) Why does decay speed up near expiry?
Near expiry, the remaining time value becomes smaller and disappears faster. That makes the premium curve steeper, especially for at-the-money options.
5) Does this calculator support American options?
No. This page uses a European-style Black-Scholes model. It is useful for education and approximation, but early exercise features are not modeled.
6) Why are volatility and rates included in a time decay tool?
Theta depends on more than time alone. Volatility, rates, dividends, moneyness, and expiry all influence how quickly premium changes as time passes.
7) What is extrinsic value?
Extrinsic value is the portion of the option premium above intrinsic value. Time decay mainly reduces this part rather than the intrinsic portion.
8) Why can the daily theta estimate differ from actual repricing?
Theta is a local slope, not a full path simulation. Repricing after several days reflects curve shape, so exact decay can differ from one-day theta multiplied repeatedly.