Problem 1

1. The price of a European put that expires in six months and has a strike price of $70 is $2.25. The underlying stock price is $65, and there are no dividends expected. Risk-free interest rates (all maturities) are 5%. Is there an arbitrage opportunity here? If so, show how much the arbitrage profit will be, and clearly depict the opening trades and the closing trades to realize that profit. If there is no arbitrage opportunity, mathematically show why there is no arbitrage opportunity.
2. The price of a European call that expires in six months and has a strike price of $132 is $1.35. The underlying stock price is $127.50, and there are no dividends expected. Risk-free interest rates (all maturities) are 5%. Is there an arbitrage opportunity here? If so, show how much the arbitrage profit will be, and clearly depict the opening trades and the closing trades to realize that profit. If there is no arbitrage opportunity, mathematically show why there is no arbitrage opportunity.