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)?

(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?

Explanation / Answer

a)

one-year risk free rate = (Payoff if price will fall *Probability of Falling + Payoff if price will rise *Probability of Rise)/Put Price -1

one-year risk free rate = (10*40% + 0*60%)/4 -1

one-year risk free rate = 0%

b)

one-year risk free rate = (Payoff if price will fall *Probability of Falling + Payoff if price will rise *Probability of Rise)/Put Price -1

one-year risk free rate = (10*50% + 0*50%)/4 -1

one-year risk free rate = 25%

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