[1](Option bound and arbitrage strategy) Recall the following model-free non-arbitrage option bounds for :

where is the initial non-dividend-paying stock price; and are American call and put options on the non-dividend paying stock with a strike expiring at time ; and is the annualized continuously compounded interest rate.

a)If the lower bound (i.e., ) is violated (i.e., is even less than ), how will you, as an arbitrageur, benefit from an arbitrage opportunity? Describe your arbitrage strategy in detail.

b)If the upper bound (i.e., ) is violated (i.e., is even greater than ), how will you, as an arbitrageur, benefit from an arbitrage opportunity? Describe your arbitrage strategy in detail.