Zomma
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Zomma is an options 'Greek' used to measure the change in gamma in relation to changes in the excitability of the underlying asset. Zomma, though ponder a third level Greek, is a first derivative of excitability, 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 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.
Alike, the vega measures how much profit or loss will be generated as the underlying asset's plied 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.
Examples of Zomma
- Zomma can be used to measure how an option's gamma will change in different market conditions. For example, an option might have a gamma of 0.75 when the spot price of the underlying asset is $50. However, if the spot price increases to $55, the gamma might increase to 0.85. Zomma can be used to measure this change in gamma.
- Zomma can be used to measure the effects of volatility on an option's delta, or sensitivity to changes in the underlying asset price. For example, a call option might have a delta of 0.60 when the underlying asset is trading at $50. If the volatility of the underlying asset increases, the delta of the call option might increase to 0.65. Zomma can be used to measure this change in delta.
- Zomma can be used to measure the effect of a change in the underlying asset price on an option's vega, or sensitivity to changes in the volatility of the underlying asset. For example, an option might have a vega of 0.20 when the underlying asset is trading at $50. If the underlying asset price increases to $55, the vega of the option might increase to 0.25. Zomma can be used to measure this change in vega.
Advantages of Zomma
Zomma is an important options Greek used to measure the change in gamma in relation to changes in the excitability of the underlying asset. It offers a number of advantages, including:
- Improved accuracy in pricing options: Zomma helps to improve the accuracy of option pricing in relation to the underlying asset. By providing a measure of the rate of change of an options Vanna, or Vomma, in relation to changes in the spot price of the underlying asset, Zomma helps to provide a more precise understanding of the effect of changes in the price of the underlying on the value of the option.
- Improved volatility management: Zomma can also help to improve volatility management. As the rate of change of an options Vanna, or Vomma, in relation to changes in the spot price of the underlying asset, Zomma helps to provide a better understanding of the impact of changes in volatility on the value of the option. This can help traders to better manage their risk exposure.
- Improved risk management: Zomma can also help to improve risk management. By providing a measure of the rate of change of an options Vanna, or Vomma, in relation to changes in the spot price of the underlying asset, Zomma helps to provide traders with a better understanding of the risks associated with their positions. This can help traders to better manage their risks, and make more informed decisions.
Limitations of Zomma
Zomma is a useful tool for traders to measure the sensitivity of an option’s value to changes in the underlying asset and volatility, however, it does have some limitations. These include:
- Difficulty in predicting future changes in volatility: Zomma measures the sensitivity of an option to changes in volatility, but cannot predict future changes in volatility. Therefore, the accuracy of Zomma is limited by the accuracy of the trader's assumptions about future volatility.
- Difficulty in calculating: Zomma is a complex calculation, and is not easy to calculate. This means that traders who do not have the correct software or knowledge may find it difficult to use Zomma to measure the sensitivity of an option to changes in volatility.
- Limited application: Zomma measures sensitivity to changes in volatility, and therefore may not be suitable for measuring sensitivity to changes in other factors such as time decay or changes in the underlying asset price.
- Limited accuracy: Zomma is a theoretical measure and does not always reflect the true sensitivity of an option to changes in volatility. This means that traders must take into account other factors such as time decay and changes in the underlying asset price when assessing the sensitivity of an option.
One approach related to Zomma is to use the Vanna-Vomma relationship. This is a relationship between the vega of an option and its vanna, which is the rate of change of vega with respect to changes in the spot price of the underlying asset.
Other approaches include:
- Gamma Risk Neutral Density (GRND): GRND is a method of measuring the changes in gamma of an option in relation to changes in the excitability of the underlying asset. It provides a way of understanding the risk associated with an options portfolio by calculating the gamma of the options portfolio at different levels of excitability.
- Vanna Volga Method: This is a method of computing the gamma of an option in relation to changes in volatility and the spot price of the underlying asset. It uses a model to capture the effects of changes in both volatility and the spot price on the option's gamma.
- Gamma-Weighted Greeks: This approach is used to calculate the gamma of an option by weighting the gamma of each strike price. This provides a more accurate measure of the gamma of an option as it takes into account the impact of changes in the spot price on the gamma at each strike price.
In summary, Zomma is an option Greek used to measure the change in gamma of an option in relation to changes in the excitability of the underlying asset. Other approaches related to Zomma include GRND, the Vanna Volga Method, and Gamma-Weighted Greeks. These approaches provide a way of understanding the risk associated with an options portfolio and more accurately measuring an option's gamma.
References
- James Chen (2018)[[1]].
- Wikipedias - Financial Derivatives Risk Management in Finance [[2]]
Author: Magdalena Stachowicz
