Formulas For Vanilla Option Greeks
See also: Black-ScholesThe Greeks of vanilla options (calls and puts) under the Black–Scholes model are calculated as follows, where (phi) is the standard normal probability density function and is the standard normal cumulative distribution function. Note that the gamma and vega formulas are the same for calls and puts.
For a given: Stock Price, Strike Price, Risk-Free Rate, Annual Dividend Yield, Time to Maturity, and Volatility ...
| Calls | Puts | |
|---|---|---|
| value | ||
| delta | ||
| vega | ||
| theta | ||
| rho | ||
| gamma | ||
| vanna | ||
| charm | ||
| speed | ||
| zomma | ||
| color | ||
| DvegaDtime | ||
| vomma | ||
| Ultima | ||
| dual delta | ||
| dual gamma | ||
where
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