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1) A one-month European put option on a non-dividend-paying stock is currently selling for $2.50....

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Finance

1) A one-month European put option on a non-dividend-paying stock is currently selling for $2.50. The stock price is $47, the strike price is $50, and the risk-free interest rate is 6% per annum. What opportunities are there for an arbitrageur?
2) What is the price of a European call option on a non-dividend-paying stock when the stock price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is three months?
3) Explain why the arguments leading to putcall parity for European options cannot be used to give a similar result for American options.

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