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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?

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    $\begingroup$ Rega and Sega are usually used for that (in FX). It is bumping the RR and BF respectively. Alternatively, vanna and Volga are closed form formulas with a similar interpretation. $\endgroup$
    – AKdemy
    Oct 23, 2023 at 16:46
  • $\begingroup$ How about skew slope exposure? Is it even useful to know that exposure/pnl? $\endgroup$ Oct 24, 2023 at 11:31

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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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