Suppose today’s stock price of Book.com is $100. With probability 60% the price

Question

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!

Explanation / Answer

STOCK PRICE=$100

PROBABILITY OF INCREASING TO $130=60%

PROBABILITY OF DECREASING TO $80=40%

EXPECTED STOCK PRICE=$130*0.60+$80*0.40=$110

STRIKE PRICE=$90

PREMIUM RECEIVED=$4

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