The current level of a broad stock market index is 1,747. Its dividend yield is 2% and the standard deviation of index returns is 50%.

An American put option on the stock expires in 0.4 years. Its strike price is $1,760. The risk-free rate is 5% (annual, continuously compounded).

Value the option using a binomial model with 2 periods of length 0.2 years each.

What is the value of d, the down-movement factor?

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

What is the option payoff in 0.4 years if the stock price went down 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?