3. The current price of a non-dividend paying stock is $30. A European put option on the stock with a strike price of $3

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3. The current price of a non-dividend paying stock is $30. A
European put option on the stock with a strike price of $31 will
expire in 6 months. The risk-free rate is flat and is at 8% per
annum with continuous compounding. Using a two-step tree with u =
1.1 and d = 0.9,
a. find the probability of the stock price moving up,
b. find the value of the put,
c. find the positions and amount needed for a riskless hedge at
each node.
d. What will the answers to questions (a) to (c) be if there is
a dividend of $0.2 in 3 months?
e. What if the put option is an American style in (d)?