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Consider the following European plain vanilla options: (1) a call with strike price K = 160,...

Consider the following European plain vanilla options: (1) a call with strike price K = 160, (2) a put with strike price K = 160, (3) a call with strike price Kc = 165, and (4) a put with strike price Kp = 155. All options have the same non-dividend-paying underlying stock and mature after one year. a) Assuming current stock price 160, stock price volatility 22%, and continuously compounded risk-free interest rate 0.49%, compute the prices of options (1)–(4) using the Black–Scholes–Merton formula showing clearly all your computations.

b) Assume a long position in options (1) and (2) and a short position in options (3) and (4). A long iron butterfly is an option strategy that comprises the aforementioned positions. i) Construct the table of the payoff profile of this strategy at maturity. ii) Calculate the implementation cost of this strategy.

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