Option Greeks Calculator Form
Example Data Table
| Scenario | Spot | Strike | Rate % | Dividend % | Volatility % | Days | Type | Delta | Gamma | Theta/Day | Vega | Rho |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Illustrative Base Case | 100 | 105 | 5 | 1 | 25 | 45 | Call | 0.323886 | 0.040914 | -0.038336 | 0.126105 | 0.037746 |
| Illustrative Hedge Check | 100 | 105 | 5 | 1 | 25 | 45 | Put | -0.674882 | 0.040914 | -0.026777 | 0.126105 | -0.090911 |
Formula Used
The calculator uses the Black Scholes framework with continuous dividend yield for European style options. It derives the Greeks from the model price sensitivity equations.
| S | Current asset price |
|---|---|
| K | Strike price |
| r | Risk free interest rate as a decimal |
| q | Continuous dividend yield as a decimal |
| σ | Implied volatility as a decimal |
| T | Time to expiry in years |
| d1 | (ln(S/K) + (r - q + 0.5σ²)T) / (σ√T) |
| d2 | d1 - σ√T |
| Call Delta | e-qTN(d1) |
| Put Delta | e-qT(N(d1) - 1) |
| Gamma | e-qTn(d1) / (Sσ√T) |
| Vega | S e-qT n(d1) √T / 100 |
| Theta | Daily decay from the Black Scholes time sensitivity equation |
| Rho | K T e-rT N(±d2) / 100 |
N(x) is the cumulative normal distribution and n(x) is the normal probability density function.
How to Use This Calculator
- Choose whether you want call or put sensitivities.
- Enter the current spot price and the option strike.
- Provide annualized risk free rate, dividend yield, and implied volatility.
- Enter days remaining until expiry.
- Set contract size and number of contracts for exposure totals.
- Press the calculate button to show results above the form.
- Review theoretical value, Greeks, d1, d2, and portfolio sensitivities.
- Use the CSV or PDF buttons to export the output.
Frequently Asked Questions
1. What does delta measure?
Delta estimates how much the option price may change when the underlying asset moves by one point, while other assumptions stay constant.
2. Why is gamma important?
Gamma shows how quickly delta changes as the asset price moves. Higher gamma means hedges may need more frequent adjustment.
3. Why is theta often negative?
Theta usually reflects time decay. As expiration approaches, options often lose time value, especially when other inputs remain stable.
4. What does vega tell me?
Vega measures price sensitivity to implied volatility. A larger vega means the option price reacts more strongly to volatility changes.
5. How should I interpret rho?
Rho estimates the option price change from a one percentage point move in interest rates. Long dated options generally show stronger rho.
6. Does this work for American options?
This implementation follows a European style Black Scholes approach. American options may differ because early exercise can affect price and Greeks.
7. Why include dividend yield?
Dividend yield influences forward value and therefore affects pricing and sensitivities. It matters most for dividend paying stocks and indexes.
8. What are exposure values?
Exposure values scale each Greek by contract size and quantity. They help estimate portfolio level sensitivity instead of single contract sensitivity.