The questions are in the screenshot. Thank you very much!

II.19. It is February 1. ABC stock is currently at 50. For each of the following positions, tell whether you would prefer that tomorrow the stock price goes up, stays the same, goes down, or it doesn't matter. Be sure to explain your reasoning. a) Long 100 shares of ABC, short 1 MAR 50 call option contract. b) Long 100 shares of ABC, long 2 MAR $5 put contracts. c) Short 1 MAR 50 call, short 1 MAR 45 put. d) Long 1 MAR 55 call, short 1 MAR 55 put, and short 100 shares of ABC. II.20. ABC stock is currently at 50. The riskless interest rate is 12%. There are 1 month European calls and puts with strike prices 45, 50 and 55 trading in the market. Consider each of the following sets of prices, then tell whether there is an arbitrage opportunity and, if so, how to exploit it. (Note that each of these is a separate case.) HINT: For one of them, there is no apparent profitable arbitrage trade. a) the 45 call is at 5 1/4 ; b) the 50 call is at 6 and the 55 call is at 2; c) the 45 put is at 6 and the 50 put is at 3; d) the 45 call is at 8, the 50 call is at 5 and the 55 call is at 1. II.21. A "Down and In" put option becomes like a regular European put option only after it is "knocked in." For this to occur, the stock price must fall below a specified level, known as the "in strike" at least once prior to the expiration date. If that never happens, the option expires worthless, regardless of where the stock price is at expiration. Assume the price of a nondividend paying stock follows a Binomial process, with u = 1.2, d = .8, and R= 1.05. The initial stock price is 100. a) What is the value of a 2 period European put with a strike price of 100? b) What is the value of a 2 period 100 strike "Down and In" put with in-strike = 94?. [Alternatives: Simple 2 period binomial valuation problems involving other such options. An American put is obviously one. Another, one of my favorites during basketball season is this: "An "In-your-face' call option is like a regular call option, except that if the stock goes up in every period, the option holder is declared 'stuffed' and the option expires worthless."]