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

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

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

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 cumulative normal distribution of d1 and N(d2) is the the cumulative normal distribution of d2.

The vomma can be interpreted as follows:

  • If Vomma is high, it indicates that the option’s Vega is highly sensitive to changes in implied volatility. The option’s value will experience more significant fluctuations with variations in implied volatility.
  • If Vomma is low, it suggests that the option’s Vega is relatively less sensitive to changes in implied volatility.

Also known as: volga, vega convexity.

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

Calculate the Vomma in Python

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

pip install financetoolkit -U

Then call get_vomma as shown below.

from financetoolkit import Toolkit

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

toolkit.options.get_vomma().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 82.5285 83.2266 83.7729 84.1863 84.4832 84.6779 84.7828 84.8089
340 86.9501 88.9058 90.6342 92.1567 93.4929 94.6604 95.6751 96.5515
345 82.9231 86.1253 89.0707 91.7752 94.2545 96.5238 98.5977 100.49
350 72.7666 76.906 80.8195 84.5108 87.9854 91.2505 94.314 97.1843
355 59.418 64.0139 68.4654 72.762 76.8965 80.8648 84.6652 88.2978
360 45.5196 50.0738 54.5902 59.0468 63.4256 67.712 71.8947 75.9648
365 32.9237 37.0405 41.222 45.4411 49.6735 53.8983 58.0974 62.2551
370 22.5959 26.0392 29.6241 33.3248 37.1171 40.9785 44.8884 48.8282
375 14.776 17.4675 20.3425 23.3816 26.5652 29.8738 33.2886 36.7917
380 9.2386 11.2195 13.3929 15.7475 18.271 20.9498 23.7698 26.7166

Parameters

get_vomma 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.
Gamma Dual Gamma Vanna Charm Vera Veta Partial Derivative

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

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