DEFINITION of Zomma
Zomma is an options 'Greek' used to measure the change in gamma in relation to changes in the volatility of the underlying asset. Zomma, though considered a third level Greek, is a first derivative of volatility, making it a second degree derivative of an underlying asset and third as it is related to the value of that underlying asset. Zomma can thus also be considered the rate of change of an option's Vanna, or Vomma, in relation to changes in the spot price of the underlying asset - where Vomma is is the rate at which the Vega of an option will react to volatility in the market, and Vega, in turn, is the change in an option's premium (price) given a change in the price of the underlying.
Zomma may also be known as an option's DgammaDvol, referring to the change ('D' for delta) in gamma per change in volatility.
BREAKING DOWN Zomma
Options traders and risk managers most often make use of the measure of Zomma to determine the effectiveness of a gamma hedged portfolio. Zomma's measure will be a measure against the change in volatility of the portfolio, or underlying assets of the portfolio.
Options portfolios (also known as 'books') have dynamic risk profiles that change on several dimensions as the price of the underlying asset moves, as time passes, and as interest rates or implied volatility changes. So for example, a book's delta will indicate how much profit or loss will be generated as the underlying prices moves up or down. But this directional risk is not linear, it has curvature in the sense that the delta value itself will become greater or smaller as the underlying price moves - this is known as the book's gamma, or change in delta given a change in the underlying price. Thus, delta is a first-derivative of the option's price and gamma is a second-derivative.
Likewise, the vega measures how much profit or loss will be generated as the underlying asset's implied volatility (IV) increases or decreases. But this too, has curvature and is sensitive to changes in the underlying price as well as to changes in volatility and time.
Which brings us to the Zomma. The Zomma measures the rate of change in the gamma relative to changes in implied volatility. Thus, if Zomma = 1.00 for an options position, a 1% increase in volatility will also increase the gamma by 1 unit, which will, in turn, increase the delta by the amount given by the new gamma. If the Zomma is high (either positive or negative), it will indicate that small changes in volatility could produce large changes in directional risk as the underlying price moves.