Calculator Inputs
Example Data Table
| Scenario | Type | Spot | Strike | Rate % | Vol % | Days | Dividend % |
|---|---|---|---|---|---|---|---|
| At-the-money call | Call | 100 | 100 | 5.00 | 20.00 | 30 | 0.00 |
| In-the-money put | Put | 92 | 100 | 4.25 | 28.00 | 45 | 1.00 |
| High-volatility call | Call | 150 | 155 | 3.75 | 42.00 | 21 | 0.50 |
Formula Used
The calculator uses the Black–Scholes theta formula for European call and put options with a continuous dividend yield assumption.
d1 = [ln(S / K) + (r - q + 0.5σ²)T] / [σ√T]
d2 = d1 - σ√T
Call Theta = -Se^{-qT}N'(d1)σ / (2√T) - rKe^{-rT}N(d2) + qSe^{-qT}N(d1)
Put Theta = -Se^{-qT}N'(d1)σ / (2√T) + rKe^{-rT}N(-d2) - qSe^{-qT}N(-d1)
Here, S is spot price, K is strike, r is risk-free rate, q is dividend yield, σ is volatility, and T is time in years.
How to Use This Calculator
- Choose whether the option is a call or a put.
- Enter the current asset price and selected strike price.
- Provide annual risk-free rate, implied volatility, and dividend yield.
- Enter remaining time to expiry in calendar days.
- Set contracts and shares per contract for position-level decay.
- Press Calculate Theta to display results above the form.
- Use the export buttons to save CSV or PDF copies.
Frequently Asked Questions
1. What does option theta measure?
Theta estimates how much an option’s value may change from one day passing, assuming other factors stay constant. Long options usually have negative theta.
2. Why is theta often negative?
Time value tends to shrink as expiration approaches. For buyers of options, this decay reduces premium, so theta is commonly negative.
3. Does this calculator handle calls and puts?
Yes. You can select either a call or a put. The calculator applies the matching Black–Scholes theta equation for the selected type.
4. What is the difference between 365-day and 252-day theta?
Some traders report daily decay using calendar days, while others use trading days. This tool shows both so you can compare conventions.
5. Why include dividend yield?
Dividend yield affects option pricing because expected dividends can reduce forward price expectations. That changes d1, d2, and theta estimates.
6. Is this result exact for every market?
No. It is a model-based estimate. Real market prices also reflect liquidity, early exercise features, volatility changes, and supply-demand effects.
7. Can I calculate position theta?
Yes. Enter number of contracts and shares per contract. The calculator multiplies per-share theta to estimate full position daily decay.
8. When is theta decay strongest?
Theta usually accelerates as expiration nears, especially for near-the-money options. Short-dated contracts often lose time value faster.