Is It Possible for an Option to Have a Negative Vega?

No, a standard call or put option will never have a negative vega. Vega is a measure of the change in an option's price for a one-point change in implied volatility, and since higher volatility always increases the chance of an option becoming profitable (for both calls and puts), it always adds value.

Therefore, vega is always positive for long options positions. However, it is possible to construct a portfolio of options (a spread or combination) that has a net negative vega.

Such a position would profit from a decrease in volatility and lose value if volatility increases.