Assuming Options to be American Options (Not European Options)

1. Suppose that the current price of an asset is $50. After six months, there are two possible values for the asset price, and after one year there are three, as follows: t = 0 t = 1/ 2 t 1 S++ = 70 S+=60 SO=50 S+- = 50 S- = 40 S-- = 30 The annual risk-free rate of interest is 5%. If there is to be no arbitrage opportunity, a) find the price of a call option on this asset, with exercise price $40 and expiration date one year from today. b) What would be the price of a put option with exercise price of $40 and expiration date one year from today? c) What will be the price of the call option after six months if the price of the underlying asset drops to $40? d) Explain why there would be an arbitrage opportunity if the price were lower than this, and describe the arbitrage portfolio

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