Questions tagged [vega]

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1answer
5k views

Link between Vega and Gamma

"The vega is the integral of the gamma profits ( ie expected gamma rebalancing P/L) over the duration of the option at one volatility minus the same integral at a different volatility...Mathematically,...
8
votes
2answers
343 views

Expectation of Gamma times S$^2$ in Black-Scholes model

Can somebody prove that: $$E[S_t^2 \times \Gamma(t,S_t)] = S_0^2 \times \Gamma(0,S_0)$$ where $S_t$ follows a lognormal process as in the Black-Scholes model, and Gamma is the second derivative $\...
3
votes
2answers
1k views

Vega and Gamma signs

Do vega and gamma always have the same sign (ie both positive or both negative)? Under what circumstances can they have opposite signs?
1
vote
2answers
3k views

Long/Short Vega and Option Positions

Why do you get long vega when you buy an option and short vega when you sell an option? I would have thought that for both buying and selling options the vega would change according to whether the ...
1
vote
1answer
541 views

Calculating option vega for vanilla call seems to be factor of 100 out

I'm using the following R code to calculate the vega on a vanilla option with the inputs S = 100, X = 100, t = 1, r = 0.005 and vol = 0.5 The vega calculated is around 39.85; I was expecting it to be ...