# Suppose that you collect following information regarding an European put option.

Suppose that you collect following information regarding an European put option.

Suppose that you collect following information regarding an European put option.
• The current price of the underlying stock is S0 = 90, and it pays no dividend.
• The put option has 1 year to maturity, with strike price K = 100.
• The continuously compounding risk-free rate is r = 0.05.
(A) Suppose you observe that the current trading price of this European put option is \$4. Prove
that there is an arbitrage opportunity and justify your answer (Note: please do not use information
supplied in part B). (15 marks)
(B) Suppose the stock price will either go up to 127.716 or go down to 70.092 at maturity but
the actual probability is unknown. Consider a one-period binomial model. What’s the implied
stock volatility in this case? (5 marks)
(C) Explain the position of a replicating portfolio that will deliver you the exact same payoff
as the European put option at maturity. (10 marks)
(D) Calculate the price of this European put option under binomial model. (5 marks)

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