Calculator inputs
Example data table
This worked example shows the same model used by the calculator, helping visitors validate inputs before pricing their own contract.
| Spot | Strike | Rate % | Volatility % | Time | Dividend % | Put value | Delta |
|---|---|---|---|---|---|---|---|
| 100.00 | 105.00 | 5.00 | 22.00 | 0.75 | 1.00 | 8.5823 | -0.4976 |
Formula used
This calculator prices a European put option with the Black-Scholes model including a continuous dividend yield.
P = K e-rT N(-d2) - S e-qT N(-d1)
d1 = [ln(S/K) + (r - q + 0.5σ2)T] / [σ√T]
d2 = d1 - σ√T
- S = current asset price
- K = strike price
- r = risk-free rate as a decimal
- q = dividend yield as a decimal
- σ = annualized volatility as a decimal
- T = time to maturity in years
- N(.) = cumulative standard normal distribution
How to use this calculator
- Enter the current asset price and your target strike price.
- Add annual risk-free rate, annual volatility, and time to maturity.
- Enter dividend yield if the asset pays continuous dividends; otherwise use zero.
- Set contracts and contract size to estimate total premium outlay.
- Choose the spot range and number of scenario points for the chart.
- Press the calculate button to show results above the form.
- Review price, Greeks, break-even, and probability measures.
- Export the scenario table and summary using the CSV or PDF buttons.
FAQs
1) What does this calculator price?
It prices a European put option, meaning exercise is assumed only at expiration. The page also reports Greeks, break-even, total premium, and scenario analysis.
2) Why do volatility and time matter so much?
Higher volatility increases uncertainty and usually raises put value. Longer time gives the option more opportunity to finish in the money, which often adds time value.
3) What is intrinsic value versus time value?
Intrinsic value is max(K − S, 0). Time value is the option premium above intrinsic value. Time value reflects uncertainty, rates, dividends, and time remaining.
4) How is break-even calculated?
For one long put at expiry, break-even equals strike price minus premium paid per unit. Below that spot level, the position starts generating positive payoff net of premium.
5) What does delta mean for a put?
Put delta is usually negative. It estimates how much the option value changes when the underlying price moves by one unit, while other assumptions remain unchanged.
6) Can I use this for dividend-paying assets?
Yes. The calculator includes a continuous dividend yield input. Set it to zero for non-dividend assets or to your annualized yield assumption when applicable.
7) Does this work for American puts?
Not exactly. American puts can be exercised early, so they may require a binomial, finite-difference, or other early-exercise model for best accuracy.
8) Why does the scenario chart show both value and expiry profit?
Model value shows today’s theoretical premium across spot levels. Expiry profit shows payoff minus current premium, helping you separate present valuation from final trade outcome.