Hey guys, I'm a physics student and don't have any real background in finance, out of interest I've been reading Hull and I'm a little confused about Vega, I hope some of you guys can help me out here.
Hull doesn't specifically say that Vega is the derivative of the option price with respect to the implied volatility, he just says it's the derivative with respect to the volatility of the underlying. Now in other books Vega is defined as the rate of change of the value of the option with respect to the implied volatility. What I don't understand about this is that implied volatility is defined as the volatility that results from the option price with all the other variables held constant, so it's rather that the option price causes implied volatility to change, doesn't it? Or can you interpret implied volatility just as the future volatility that the market expects based on the option price? So if e.g actual volatility increases in the next week, can the increase in the value of the option as a result of that increased volatility be interpreted as vega?