I have read several articles about local volatility and implied volatility, but I am still confused with the difference between the two.
Please correct me if I am wrong: Implied volatility is the constant volatility back-solved from the BS model with the current option price and market parameters (e.g. interest rate, spot price, strike, etc). Meanwhile, local volatility is also the volatility calculated via BS model, but additionally it assumed volatility is a function the underlying price and time when we calculate the local volatility.
So my first question: is my interpretation above correct? (I am looking for an intuitive explanation for two concepts.)
And second: if local volatility is calculated from BS model, how can it be calculated at the same time considering it is a function of the underlying price and time?
I do not have a quantitative background, so I am looking for an easy-to-understand explanation for above questions.