What is Vomma?
Vomma is the rate at which the vega of an option will react to volatility in the market. It belongs to a group of measures known as the “Greeks,” which are fundamental in pricing options.
Key Takeaways
- Vomma is the rate at which the vega of an option will react to volatility in the market.
- Vomma is a second-order derivative for an option’s value and demonstrates the convexity of vega.
- 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 explained by vega’s convexity.
Vomma and vega are crucial in identifying profitable option trades. They work together, providing detailed information about an option’s price sensitivity to market changes and significantly influence the Black-Scholes pricing model for option pricing.
As a second-order Greek derivative, vomma offers insights into how vega will change with the implied volatility (IV) of the underlying asset. If a positive vomma is calculated and volatility increases, vega will also rise. Conversely, if the volatility decreases, a positive vomma indicates a drop in vega. Interestingly, a negative vomma illustrates the opposite scenario with volatility changes.
Generally, investors with long options should seek a high, positive vomma value, while those with short options might look for a negative vomma.
The formula for calculating vomma is as follows:
Vomma = \frac{\partial
u}{\partial \sigma} = \frac{\partial^2 V}{\partial \sigma^2}
Vega and vomma are crucial in assessing the sensitivity of the Black-Scholes option pricing model to variables affecting option prices. These metrics are important considerations when making investment decisions.
Vega: The Complementary Greek
Vega helps traders understand a derivative option’s sensitivity to volatility from the underlying asset. It quantifies the expected price change in an option for a 1% change in the volatility of the underlying instrument. A positive vega indicates a rise in the option price, while a negative vega signals a decrease. A vega-neutral position helps traders mitigate some of the risks tied to implied volatility.
Vega is measured in whole numbers, ranging typically from -20 to 20. Longer time periods usually lead to a higher vega, highlighting potential gains or losses. For example, a vega of 5 on a $100 stock implies a $5 loss for each point decrease in implied volatility, and a $5 gain for each point increase.
The formula for calculating vega is detailed below:
u = S \phi(d1) \sqrt{t}
\\
\text{with:} \quad \phi(d1) = \frac{e^{-\frac{d1^2}{2}}}{\sqrt{2\pi}}
\text{and} \quad d1 = \frac{\ln\left(\frac{S}{K}\right) +
\left( r + \frac{\sigma^2}{2} \right)t}{\sigma \sqrt{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
Related Terms: Delta, Gamma, Theta, Rho, Implied Volatility, Black-Scholes Model.
