Consider a derivative whose payoff is as follows:

A$-$ The derivative will expire immediately when the stock price increases by more than $50\%$ or decreases by more than $30\%$ as compared to the current stock price, and investors will get the stock price at the time of expiration.

B$-$ If the stock price never increases by more than $50\%$ or decreases by more than $30\%$ within one$-$year, then investors get the stock price after one year.

What is the value of this derivative? Show the evolution path of its value.