Calculator Form
This page uses a single-column page flow. The calculator grid switches to three columns on large screens, two on medium screens, and one on mobile.
Example Data Table
Sample scenarios below show how the model reacts to different inputs.
| Scenario | Type | Spot | Strike | Years | Volatility | Rate | Dividend | Model Price | Delta |
|---|---|---|---|---|---|---|---|---|---|
| Sample A | Call | 105 | 100 | 0.75 | 22% | 4.50% | 1.00% | 11.9721 | 0.6825 |
| Sample B | Put | 92 | 100 | 0.50 | 28% | 4.00% | 0.00% | 10.8815 | -0.5875 |
| Sample C | Call | 150 | 145 | 1.25 | 18% | 5.00% | 1.50% | 17.6897 | 0.6739 |
Formula Used
d2: d2 = d1 - σ√T
Where S is spot price, K is strike price, r is risk-free rate, q is dividend yield, σ is annualized volatility, T is time in years, and N(·) is the cumulative normal distribution.
How to Use This Calculator
- Choose whether you want to value a call or a put.
- Enter the current underlying price and the strike price.
- Input time to maturity in years, annualized volatility, risk-free rate, and dividend yield.
- Add contracts and contract size to scale the position totals.
- Optionally enter a premium paid if you want payoff and break-even based on your actual trade cost.
- Press Calculate Option Price to show the result above the form and below the header.
- Use Download CSV for spreadsheet work or Download PDF from the result panel for reporting.
- Review the Plotly chart to inspect expiry payoff behavior across possible underlying prices.
FAQs
1. What pricing model does this calculator use?
It uses the Black-Scholes framework with continuous dividend yield. The model estimates theoretical value, Greeks, break-even, and payoff for long European-style call and put positions.
2. Why does volatility matter so much?
Higher volatility increases the probability of large price swings before expiry. Because options benefit from wider possible outcomes, their theoretical value usually rises when implied volatility rises.
3. What does delta tell me?
Delta estimates how much the option price may change for a one-unit move in the underlying. It also gives a rough directional exposure for the position.
4. Why is theta often negative?
Long options lose time value as expiration approaches, all else equal. Negative theta reflects that daily decay in extrinsic value.
5. What is the difference between model value and premium paid?
Model value is the theoretical estimate from the formula. Premium paid is your actual trade cost. If you enter your premium, payoff and break-even use that amount instead.
6. Does this handle American exercise?
No. This version is designed around European-style pricing assumptions. It is still useful for quick analysis, but early exercise features are not modeled directly.
7. What does the risk-neutral ITM probability mean?
It is a model-based probability under risk-neutral assumptions, not a guaranteed real-world forecast. Use it as a pricing reference, not as a certainty estimate.
8. When should I export CSV or PDF?
Use CSV for spreadsheet analysis, audit trails, or dashboards. Use PDF when you need a clean snapshot for reports, client notes, or internal review documents.