a. You are an options dealer who deals in non-publicly traded options. One of your clients wants to purchase a one-year European call option on Deutsche Bank shares with an exercise price of $30. Another dealer is willing to write a one-year European put option on Deutsche Bank shares with an exercise price of $30, and sell you the put option for a price of $3.50 per share. If Deutsche Bank pays no dividends and is currently trading for $25 per share, and if the risk-free interest rate is 7.5%, what is the lowest price you can charge for the call option and guarantee yourself a profit? b. What are the key inputs that determine an options price? Please explain each input and its key function. c. What is the difference between a European option and an American option?