Measuring Option Exposure to Volatility Skew and Convexity
Summary
The note discusses how options traders describe exposure to changes in implied volatility skew and volatility convexity. Skew refers to differences in implied volatility across strikes, such as between out-of-the-money puts and calls. Traders may characterize a position as long or short skew according to how it responds when those relative volatility levels change.
For volatility convexity, the answer identifies vomma, also called volga, as the sensitivity of vega to implied volatility, or equivalently the second derivative of option value with respect to volatility. It offers terminology and conceptual definitions, but does not explain a standardized skew unit, provide a complete method for calculating position-level P&L, or discuss practical conventions and model dependence. The treatment is therefore introductory and leaves the question about attributing realized P&L largely unanswered.
Key ideas
- Implied volatility skew describes differences in volatility across option strikes.
- Long or short skew describes how a position responds to changes in those relative volatility levels.
- Vomma, also called volga, measures how vega changes as implied volatility changes.
- The note does not provide a full procedure for attributing P&L to skew and convexity.
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Full text
# Smile Skew and Convexity Exposure # Smile Skew and Convexity Exposure We're all familiar with the Greeks (Delta, Gamma, Vega, etc.). They provide a quantified exposure to various risk factors. But what about skew and convexity? Is there a similar standardized way to express exposure to smile skew and convexity in terms of specific units or metrics? For instance, with Delta, we can say we have an exposure of 'X' Delta units to the underlying price. Can we express skew and convexity exposure in a similar manner? Additionally, how do traders typically compute the P&L attributed to these exposures? ## Answer by Amit Kumar Jha (score 1) https://quant.stackexchange.com/a/77118 skew and convexity are important concepts in the world of options trading, and traders do have ways to quantify exposure to these factors. Skew: Definition: Skew measures the difference in implied volatility (IV) between out-of-the-money, at-the-money, and in-the-money options. Negative skew implies that out-of-the-money puts have higher IV than out-of-the-money calls, which is typical for equity index options. Metric: The term "skew" itself can be used as a metric. For instance, if one says the skew is 2%, it means that the IV of an out-of-the-money put is 2% higher than that of an out-of-the-money call. So, when traders talk about their exposure to skew, they might say they are "long skew" or "short skew," indicating their positions will benefit from an increase or decrease in skew, respectively. Convexity (or Vomma or Volga): Definition: Convexity in the context of options refers to the rate of change of an option's vega with respect to changes in volatility. It measures the sensitivity of an option's vega to changes in implied volatility. This is crucial for traders who take positions in options with different strike prices and maturities. Metric: Vomma (or Volga) is the metric used to quantify convexity. It is the second derivative of the option price with respect to volatility. If a trader says they have a Vomma of 50, it means for every 1% increase in volatility, the vega of their position will change by 50 units. Traders might express their positions as being "long convexity" or "short convexity
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