Veta
Calculate the veta of an option based on the Black Scholes Model. The Black Scholes Model is a mathematical model used to estimate the price of European-style options. The veta is the rate of change of the vega with respect to the time to expiration.
The veta calculation is the theoretical value of the veta. The actual veta can differ from this value due to several factors such as the volatility of the underlying asset, the time to expiration, the risk free rate and more.
The formula is as follows:
\[d_{1} = (\ln(S / K) + (r - q + (\sigma ^{2}) / 2) \cdot t) / (\sigma \cdot \sqrt{t})\] \[d_{2} = d_{1} - \sigma \cdot \sqrt{t}\] \[\text{Veta} = S \cdot e ^{- q \cdot t} \cdot N'(d_{1}) \cdot \sqrt{t} \cdot (q + ((r - q) \cdot d_{1}) / (\sigma \cdot \sqrt{t}) - (1 + d_{1} \cdot d_{2}) / (2 \cdot t)) / (100 \cdot 365)\]Where S is the stock price, K is the strike price, r is the risk free rate, q is the dividend yield, σ is the volatility, t is the time to expiration, N’(d1) is the standard normal probability density at d1 and N(d2) is the cumulative normal distribution of d2.
The formula as usually published carries a leading minus sign because it differentiates with respect to the time to maturity, which runs opposite to elapsed calendar time. That sign is absorbed here so that Veta, like Theta, Charm and Color, measures the change per unit of time that passes: a long option loses Vega as expiry approaches, so its Veta is negative.
It is common practice to divide the mathematical result of veta by 100 times the number of days per year to reduce the value to the percentage change in vega per one day. This is also done here.
The Veta can be interpreted as follows:
- If Veta is positive, it indicates that the option’s Vega is becoming more positive over time. In other words, the option is gaining sensitivity to changes in implied volatility as time passes.
- If Veta is negative, it suggests that the option’s Vega is becoming more negative over time. The option is losing sensitivity to changes in implied volatility as time passes.
Also known as: vega time decay.
No programming experience? With the Finance Toolkit MCP server, AI assistants such as Claude and ChatGPT can calculate the Veta for you. Just ask in plain English.
Calculate the Veta in Python
The Veta is available in the Options module of the open-source Finance Toolkit. Install it with:
pip install financetoolkit -U
Then call get_veta as shown below.
from financetoolkit import Toolkit
toolkit = Toolkit(["AAPL", "ASML"], api_key="FINANCIAL_MODELING_PREP_KEY")
toolkit.options.get_veta().loc["AAPL"]
Which returns:
| Strike Price | 2026-07-24 | 2026-07-25 | 2026-07-26 | 2026-07-27 | 2026-07-28 | 2026-07-29 | 2026-07-30 | 2026-07-31 |
|---|---|---|---|---|---|---|---|---|
| 335 | 1170.49 | 1152.48 | 1134.42 | 1116.45 | 1098.68 | 1081.18 | 1064.01 | 1047.21 |
| 340 | 1086.11 | 1080.12 | 1072.76 | 1064.34 | 1055.09 | 1045.2 | 1034.83 | 1024.12 |
| 345 | 949.052 | 955.916 | 960.422 | 962.917 | 963.7 | 963.03 | 961.127 | 958.182 |
| 350 | 782.262 | 800.007 | 814.975 | 827.465 | 837.751 | 846.079 | 852.672 | 857.73 |
| 355 | 609.865 | 634.686 | 656.928 | 676.767 | 694.38 | 709.94 | 723.614 | 735.564 |
| 360 | 451.066 | 478.669 | 504.341 | 528.109 | 550.028 | 570.166 | 588.605 | 605.433 |
| 365 | 317.447 | 344.156 | 369.769 | 394.195 | 417.377 | 439.286 | 459.915 | 479.276 |
| 370 | 213.191 | 236.54 | 259.579 | 282.151 | 304.131 | 325.422 | 345.951 | 365.664 |
| 375 | 136.99 | 155.808 | 174.905 | 194.113 | 213.286 | 232.298 | 251.039 | 269.421 |
| 380 | 84.4307 | 98.5912 | 113.375 | 128.643 | 144.263 | 160.113 | 176.082 | 192.07 |
Parameters
get_veta accepts the following parameters:
- start_date (str | None, optional): The start date which determines the stock price. Defaults to None which means it will use the most recent date.
- strike_price_range (float): The percentage range to use for the strike prices. Defaults to 0.25 which equals 25% and thus results in strike prices from 75 to 125 if the current stock price is 100.
- strike_step_size (int): The step size to use for the strike prices. Defaults to 5 which means that the strike prices will be 75, 80, 85, 90, 95, 100, 105, 110, 115 and 120 if the current stock price is 100.
- expiration_time_range (int): The number of days to use for the time to expiration. Defaults to 30 which equals 30 days.
- risk_free_rate (float, optional): The risk free rate to use for the calculation. Defaults to None which means it will use the current risk free rate.
- dividend_yield (float, optional): The dividend yield to use for the calculation. Defaults to None which means it will use the current dividend yield.
- show_input_info (bool, optional): Whether to show the input information. Defaults to False.
- rounding (int | None, optional): The number of decimals to round the results to. Defaults to 4.
- standardize (bool, optional): Whether to standardize (Z-Score) the result across the time to expiration columns for each ticker and strike price. Defaults to False.
Related Second-Order Greeks
The Options module page introduces the module, and the sidebar lists all of its functions.