The current price of a non-dividend-paying stock is $1,586 and you expect the stock price to either go up by a factor of 1.107 or down by a factor of 0.925 each period for 2 periods over the next 0.4 years. Each period is 0.2 years long.

A European call option on the stock has a strike price of $1,586 and expires in 0.4 years. The risk-free rate is 6% (annual, continuously compounded).

What is the risk-neutral probability of an up movement?

What is the option payoff in 0.4 years if the stock price went up twice in a row?

What is the value of the option in 0.2 years if the stock price has gone up once?

What is the value of the option in 0.2 years if the stock price has gone down once?

What is the current value of the option?