How Gamma and Vega Exposures Differ in Option Positions
Summary
The document distinguishes gamma exposure, associated with realized movements in the underlying, from vega exposure, which reflects sensitivity to changes in implied volatility. A plain vanilla option generally carries both exposures, but combining options can produce a position whose gamma and vega have opposite signs.
A calendar spread illustrates the distinction: buying a shorter-dated at-the-money call and selling a longer-dated call on the same underlying can create positive gamma and negative vega, because the short-dated option contributes relatively more gamma while the longer-dated option contributes relatively more vega. The position may benefit from realized volatility before the near-term option expires and from a decline in implied volatility. The discussion also gives a Black–Scholes relationship linking vega and gamma as a function of volatility, spot price, and time to expiry. These are framework-specific sensitivities; the spread’s behavior depends on its construction and market conditions, and the formula cited assumes Black–Scholes conditions.
Key ideas
- Gamma measures second-order option price sensitivity to the underlying price, while vega measures sensitivity to volatility.
- Long gamma is associated with realized movement; long vega benefits from rising implied volatility.
- Plain vanilla options typically expose holders to both gamma and vega.
- A calendar spread can combine positive gamma with negative vega because the maturities contribute differently.
- The stated vega–gamma relationship applies under Black–Scholes assumptions.
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Full text
# Long Gamma vs Vega
# Long Gamma vs Vega
What is the difference between being long gamma and being long Vega? I understand that gamma is the vol of delta and that vega is the vol of the underlying. However, I have also found that being long gamma and long vega basically means being long options. In that case, what is the difference between the two?
Cheers.
## Answer by AlRacoon (score 24, accepted)
https://quant.stackexchange.com/a/38372
Long gamma is being long realized volatility. Long vega is being long implied volatility. Long gamma positions benefit when realized volatility goes up or the actual underlying has volatility. Long vega positions benefit when the price of volatility goes up.
Being long plain vanilla options, one is long both gamma and long vega. However, this is not so if one starts to combine options in strategies. One can construct positions where one is long gamma and short vega.
A simple example would be a simple calendar spread--if one is long an at-the-money call with short maturity, one is long gamma and long vega. If one shorts an at-the-money longer dated maturity call on the same underlying, one is short gamma and short vega. However, the short longer dated call will be less long gamma than the shorter dated one; and short more vega than the shorter dated one. The combined position will be long gamma and short vega. The position will benefit if realized volatility goes up before the shorter dated call expires, and if implied volatility goes down.
## Answer by Quantuple (score 11)
https://quant.stackexchange.com/a/38365
Vega (denoted by $\nu$ in what follows) is the first order sensitivity of the option price with respect to volatility $\sigma$. Gamma (denoted by $\Gamma$ in what follows), is the second order sensitivity of the option price with respect to the underlying spot price $S$.
Because for a semi-martingale $(S_t)_{t \geq 0}$ there is a direct link between the variance of the random variable $S_t$ for any fixed $t$ and its quadratic variation over $[0,t]$, it is only logical that there exists a link between Vega and Gamma.
Under BS assumptions, one can show that for an option evaluated at $t$ with time to maturity $\tau = T-t$ $$\nu(\tau) = \Gamma(\tau) \, \sigma S_t^2 \tau$$ see Appendix A of Chapter 5 of Bergomi's book "Stochastic Volatility Modeling" for a demonstartion and this Wiki page to see that it indeed holds under BS.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.