Calculate the vega 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 vega is the rate of change of the option price with respect to the volatility of the underlying asset.

The vega calculation is the theoretical value of the vega. The actual vega 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:

\[d_{1} = (\ln(S / K) + (r - q + (\sigma ^{2}) / 2) \cdot t) / (\sigma \cdot \sqrt{t})\] \[\text{Vega} = S \cdot e ^{- q \cdot t} \cdot N'(d_{1}) \cdot \sqrt{t} / 100\]

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 division by 100 expresses Vega per 1 percentage point change in volatility, the usual market quote. The higher order volatility Greeks (Vanna, Vomma, Zomma, Vera, Ultima) are reported unscaled, per 1.00 of volatility; only Vega and Veta carry this factor.

The Vega can be interpreted as follows:

  • If Vega is positive, it indicates that the option value will increase as the volatility increases, and vice versa.
  • If Vega is negative, it implies that the option value will decrease as the volatility increases, and vice versa.

Note that the vega of a call option and put option are equal to each other.

Also known as: option sensitivity to volatility changes.

No programming experience? With the Finance Toolkit MCP server, AI assistants such as Claude and ChatGPT can calculate the Vega for you. Just ask in plain English.

Calculate the Vega in Python

The Vega is available in the Options module of the open-source Finance Toolkit. Install it with:

pip install financetoolkit -U

Then call get_vega as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(["AAPL", "ASML"], api_key="FINANCIAL_MODELING_PREP_KEY")

toolkit.options.get_vega().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 0.1516 0.1603 0.1689 0.1773 0.1856 0.1938 0.2019 0.2098
340 0.1134 0.1215 0.1296 0.1376 0.1456 0.1535 0.1613 0.169
345 0.081 0.0882 0.0954 0.1026 0.1098 0.1171 0.1243 0.1315
350 0.0555 0.0614 0.0675 0.0736 0.0799 0.0862 0.0926 0.099
355 0.0364 0.0411 0.0459 0.051 0.0561 0.0614 0.0668 0.0722
360 0.023 0.0265 0.0302 0.034 0.0381 0.0423 0.0466 0.0511
365 0.014 0.0164 0.0191 0.022 0.025 0.0283 0.0316 0.0352
370 0.0082 0.0099 0.0117 0.0138 0.016 0.0183 0.0208 0.0235
375 0.0046 0.0057 0.007 0.0084 0.0099 0.0116 0.0134 0.0153
380 0.0025 0.0032 0.004 0.0049 0.0059 0.0071 0.0083 0.0097

Parameters

get_vega 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 dividend yield as obtained through annual historical data.
  • 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.
Delta Dual Delta Theta Rho Epsilon Lambda

The Options module page introduces the module, and the sidebar lists all of its functions.

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