Vomma: What it is, How it Works, Formula

What Is Vomma?

Vomma is the rate at which the vega of an option will react to volatility in the market. Vomma is part of the group of measures—such as delta, gamma, and vega—known as the "Greeks," which are used in options pricing.

Understanding Vomma

Vomma is a second-order derivative for an option’s value and demonstrates the convexity of vega. A positive value for vomma indicates that a percentage point increase in volatility will result in an increased option value, which is demonstrated by vega's convexity.

Vomma and vega are two factors involved in understanding and identifying profitable option trades. The two work together in providing detail on an option's price and the option price’s sensitivity to market changes. They can influence the sensitivity and interpretation of the Black-Scholes pricing model for option pricing.

Vomma is a second-order Greek derivative, which means that its value provides insight on how vega will change with the implied volatility (IV) of the underlying instrument. If a positive vomma is calculated and volatility increases, vega on the option position will increase. If volatility falls, a positive vomma would indicate a decrease in vega. If vomma is negative, the opposite occurs with volatility changes as indicated by vega’s convexity.

Generally, investors with long options should look for a high, positive value for vomma, while investors with short options should look for a negative one.

The formula for calculating vomma is below:

$\begin{aligned} \text{Vomma} = \frac{ \partial \nu}{\partial \sigma} = \frac{\partial ^ 2V}{\partial\sigma ^ 2} \end{aligned}$Vomma=∂σ∂ν​=∂σ2∂2V​​

Vega and vomma are measures that can be used in gauging the sensitivity of the Black-Scholes option pricing model to variables affecting option prices. They are considered along with the Black-Scholes pricing model when making investment decisions.

Vega

Vega helps an investor to understand a derivative option’s sensitivity to volatility occurring from the underlying instrument. Vega provides the amount of expected positive or negative change in an option’s price per 1% change in the volatility of the underlying instrument. A positive vega indicates an increase in the option price and a negative vega indicates a decrease in the option price.

Vega is measured in whole numbers with values usually ranging from -20 to 20. Higher time periods result in a higher vega. Vega values signify multiples representing losses and gains. A vega of 5 on Stock A at $100, for example, would indicate a loss of $5 for every point decrease in implied volatility and a gain of $5 for every point increase.

The formula for calculating vega is below:

$\begin{aligned} &\nu = S \phi (d1) \sqrt{t} \\ &\text{with} \\ &\phi (d1) = \frac {e ^ { -\frac{d1 ^ 2}{2} } }{ \sqrt{2 \pi} } \\ &\text{and} \\ &d1 = \frac { ln \bigg ( \frac {S}{K} \bigg ) + \bigg ( r + \frac {\sigma ^ 2}{2} \bigg ) t }{ \sigma \sqrt{t} } \\ &\textbf{where:}\\ &K = \text{option strike price} \\ &N = \text{standard normal cumulative distribution function} \\ &r = \text{risk free interest rate} \\ &\sigma = \text{volatility of the underlying} \\ &S=\text{price of the underlying} \\ &t = \text{time to option's expiry} \\ \end{aligned}$​ν=Sϕ(d1)t​withϕ(d1)=2π​e−2d12​​andd1=σt​ln(KS​)+(r+2σ2​)t​where:K=option strike priceN=standard normal cumulative distribution functionr=risk free interest rateσ=volatility of the underlyingS=price of the underlyingt=time to option’s expiry​