# What is option vomma?

By Simon Gleadall, CEO of Volcube.

Vomma is an option Greek which tells us the change in option vega for a change in implied volatility. Vomma is a *2nd order Greek*, which means it tells us how another Greek changes, rather than how the option’s value changes directly, when something else changes. Let’s take a simple example. Consider an option with a value of $1.50 that has 5 vega. This means that if implied volatility increases by 1%, the option will rise in value by 5 cents, to $1.55. However, this may not be the whole story. If the option also has vomma, then its vega will also change as the implied vol changes. Suppose the option has a normalized vomma of 3. This means that for a 1% change in implied vol, the option *vega* will increase by 3; i.e. from 5 to 8. So, going back to our option worth $1.50, if the implied vol rises by 1%, its value will actually increase by an amount closer to 6.5 cents, to $1.565. Why this amount? Well, this is the *average* vega the option has whilst the implied vol is rising. We can therefore take this as an approximation of the option vega during the change in implied volatility. A helpful analogy might be a car that is travelling at 5 m.p.h. After 1 hour, it will have travelled 5 miles. But if the car is also accelerating at 3 m.p.h *per hour*, then it will travel further than just 5 miles in an hour. You can think of the speed of the car as the vega of the option and the vomma as the acceleration.

And this cuts both ways. Vomma is a positive function, which means if an option has positive vomma and implied volatility *falls*, then the option vega will fall. For the option in our example, if vol falls by 1%, the vega of the option to begin with is 5 but by the time the vol has fallen fully, it has dropped to just 2 (because it has 3 vomma). So we could say the option has an average vega over the change in implied vol of about 3.5 and so we would predict a new value of $1.465.

Confusingly, vomma is sometimes also known as alpha (and indeed when you trade on the Volcube options simulator, vomma is labelled as alpha).

## Which options have vomma?

A lot of Greeks tend to be concentrated in the at-the-money options; these have the highest ‘optionality’ and therefore the highest vega, gamma, theta etc. But, vomma is one of the exceptions. Vomma is higher for wing options (i.e. not at-the-money options). In fact, vomma tends to be highest in options with an absolute delta of approximately 15%. One way to understand why wing options have higher vomma is to realise that higher implied vol tends to make wing options more like at-the-money options. If implied vol was infinite, *all* options would be at-the-money options. And since at-the-money options have the highest vega, then the more wing options tend to be like at-the-money options, the higher their vega must be. In other words, higher implied vol means higher vega, and that is identical to saying these options have positive levels of vomma.

## The risks associated with option vomma

The risks associated with option vomma tend to become very apparent in large vol moves. For small, day-to-day changes in implied volatility, the vomma risk is usually reasonably muted. But when implied volatility moves a large amount, the effect of vomma can be considerable. For example, suppose we are long $50,000 of vega and short $100,000 of vomma. This might be the result of owning some at-the-money options and being short wing options (either out-of-the-money calls or puts or both). Now suppose that implied vol increases by 5%. You might think this is good news because we are long vega. 5*$50,000 should mean we make $250,000 in profit from our vega. But hold on; what about the vomma? Our vomma position means that we will actually become *short* vega reasonably quickly. Our wing options came more into play, as the implied vol rises. This wipes out our long vega position and in fact we will lose money overall from the 5% increase in vol.

This shows how vomma can be a very important Greek to consider. It adds another dimension to our risk management; with options it is rarely adequate to simply consider the first order Greeks because they themselves are subject to change. This is at the heart of understanding option risk management. It is not simply knowing your Greeks; you need to understand how and why they change as the different variables change (spot price, implied vol, time to expiry etc.).

You can practise managing and learning about vomma using the Volcube simulator. Trade some games where you accumulate a position with wing options, through outrights or strangles and also with at-the-money options through straddles or outrights. Notice how your vomma (i.e. your alpha) varies and estimate the effect this will have on your overall vega as the implied vol changes. Mastering vomma is essential for advanced understanding of options trading.

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