You are valuing a call option using a binomial pricing model. The stock is currently priced at $82. The option is set to expire in three years. The strike price on the option is $88 and the risk-free rate is 4.5%. You estimate the percentage change in stock price for an up move is 120% and 90% for a down move.

What is the up move probability? What is the probability of this option expiring worthless? What is the expected payoff on this option at time 3? What is the call option value today?