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Suppose today's stock price of Book.com is $100. With probability 60% the price will rise to $130 in one year and with probability 40% it will fall...

Suppose today's stock price of Book.com is $100. With probability 60% the price will rise to $130 in one year and with probability 40% it will fall to $80 in one year. A European put option with a strike price of $90 and a time to expiration of one year sells at $4.
(a) What is the one-year risk free rate implied by no-arbitrage (hint draw a binomial tree as we did in class)?
(b) What would be the no-arbitrage risk free rate if with a probability of 50% the price increases and with a probability of 50% it decreases, keeping all other values constant?
Explain!

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