Suppose that a stock price starts at $$800$ at time $0.$ At time $1($one day

later$),$ the stock will either be worth $$850$ or $$650.$ If the stock is worth $$850$ at time $1,$ then the stock will either be worth $$1000$ or $$800$ at time $2.$ And If the stock is worth $$650$ at time $1,$ then the stock will either be worth $$750$ or $$200$ at time $2.$ Consider a European call option with strike price $$400$ and expiry time $2.$ Suppose the stock price at time $1$ is $$650$ and you plan on offering the above European call option to the people in financial market. What is the fair price that you should charge based on $$Fair Market $($No$-$Arbitrage$)$ principle?