Problem 5. (7+6 pts) The payoff at maturity T of a cash-or-nothing call option with strike K is 1 is S(T) > K, and 0 otherwise. You are given the following prices of 3-month European plain vanilla call options on the XYZ stock, whose current price is $36. Assume zero rates and dividends. Strike Call Price 34 2.90 35 2.32 36 1.80 37 1.37 38 1.00 a (a) Establish upper and lower no-arbitrage bounds for the price of a cash-or-nothing call option on the same stock struck at $36. Establish upper and lower no- arbitrage bounds for the price of a cash-or-nothing put option on the same stock struck at $36. (b) Establish upper and lower no-arbitrage bounds for the price of an option that pays $1 if the final stock price is between $35 and $37. Problem 5. (7+6 pts) The payoff at maturity T of a cash-or-nothing call option with strike K is 1 is S(T) > K, and 0 otherwise. You are given the following prices of 3-month European plain vanilla call options on the XYZ stock, whose current price is $36. Assume zero rates and dividends. Strike Call Price 34 2.90 35 2.32 36 1.80 37 1.37 38 1.00 a (a) Establish upper and lower no-arbitrage bounds for the price of a cash-or-nothing call option on the same stock struck at $36. Establish upper and lower no- arbitrage bounds for the price of a cash-or-nothing put option on the same stock struck at $36. (b) Establish upper and lower no-arbitrage bounds for the price of an option that pays $1 if the final stock price is between $35 and $37