Question

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. Assuming current stock price 160, stock price volatility 22%, and continuously compounded
risk-free interest rate 0.49%.

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

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Construct the table of the payoff profile of this strategy at maturity.

Answer 1

Step 1: Calculate the Option Price of the given options using Black-Scholes. Then calculate the Future Value of the Option Value for t=1 Year.

Step 2: Construct the Payoff Profile for individual options: Call= Max(S-K,0); Put = Max (K-S,0);