Part I.

Indicate whether each of the following two statements below is true, false or uncertain and justify your response.

1. It is theoretically impossible for an out-of-money European call and an in-the-money European put to be trading at the same price. Both options are written on the same non-dividend paying stock.
2. By simultaneously buying a call and short-selling the underlying asset, we can create a synthetic short position in the put.

Part II.

A 3-month European put option on a non-dividend-paying stock is currently selling for $3.50. The stock price is $47.0, the strike price is $51, and the risk-free interest rate is 6% per annum (continuous compounding). Analyze the situation to answer the following question:

If there is no arbitrage opportunity in above case, what range of put option price will trigger an arbitrage opportunity? If there is an arbitrage opportunity in the above case, please provide one possible trading strategy to take advantage of this opportunity and show your trading results.