Calculator Inputs
Example Data Table
| Scenario | Type | Structure | Spot | Strike | Payout | Rate % | Vol % | Time |
|---|---|---|---|---|---|---|---|---|
| Baseline | Call | Cash | 100 | 100 | 10 | 5 | 20 | 0.50 |
| Higher Volatility | Call | Cash | 100 | 100 | 10 | 5 | 35 | 0.50 |
| Bearish Setup | Put | Cash | 92 | 100 | 15 | 4 | 28 | 0.75 |
| Asset Binary | Call | Asset | 105 | 100 | 1 | 4.5 | 22 | 0.25 |
Formula Used
Black-Scholes digital pricing is used for European-style binaries. Let:
d1 = [ln(S/K) + (r - q + 0.5σ²)T] / (σ√T)
d2 = d1 - σ√T
Cash-or-nothing call = Qe-rTN(d2)
Cash-or-nothing put = Qe-rTN(-d2)
Asset-or-nothing call = QS e-qTN(d1)
Asset-or-nothing put = QS e-qTN(-d1)
Here, S is spot price, K strike price, Q payout scale, r risk-free rate, q dividend yield, σ volatility, and T time to expiry. Greeks are estimated numerically with central differences for robust scenario analysis.
How to Use This Calculator
- Select whether you want a call or put digital structure.
- Choose cash-or-nothing or asset-or-nothing pricing.
- Enter spot, strike, payout amount, rate, dividend yield, volatility, and years to expiry.
- Set the number of contracts to scale position value.
- Submit the form to view price, Greeks, probability, forward price, and model parameters above the form.
- Use the export buttons to save results as CSV or PDF for reports, study notes, or trade reviews.
Frequently Asked Questions
1. What does a digital option pay?
A digital option pays a fixed cash amount or a defined asset-based amount if the expiry condition is met. Otherwise, it pays nothing.
2. What is the difference between cash and asset binaries?
Cash binaries return a fixed amount at expiry. Asset binaries return an amount linked to the underlying asset if the option finishes in the money.
3. Why are Greeks useful here?
Greeks show how sensitive the option value is to changes in spot, volatility, time, and rates. That helps measure risk quickly.
4. Can I use this for American-style binaries?
No. This setup uses European-style Black-Scholes logic. Early exercise features need different models or numerical methods.
5. What does the probability output represent?
It estimates the risk-neutral probability of finishing in the money at expiry. It is model-based, not a guaranteed real-world prediction.
6. Why can digital option gamma look extreme?
Digital payoffs change abruptly near the strike. Because of that, small spot moves can create sharp changes in delta and gamma.
7. When should I export CSV or PDF?
Use CSV for spreadsheet analysis and PDF for reports, homework, client notes, or saved trade documentation.