Question

Construct an Iron Butterfly strategy using a table and draw the profit-loss diagram. An Iron Butterfly requires that one buy an OTM put with X1 , sell another ATM put with X2 , sell an ATM call with X2 , and buy an OTM call with X3 . X1 , X2 , and X3 are evenly spaced. Explain what are the similarities and differences between a Butterfly and an Iron Butterfly

Answer 1

In order to create the profit loss diagram, we need to assign values to each of the variable X1, X2, X3. Let's create the Iron Butterfly as follows:

• Buy an OTM put with X1 = $ 50 at a premium or price of P1 = $ 0.30; Resultant gain / (loss) = max (X1 - X, 0) - P1 = max (50 - X, 0) - 0.30
• Sell another ATM put with X2 = $ 60 at a premium or price of P2 = $ 3; Resultant gain / (loss) = - max (X2 - X, 0) + P2 = - max (60 - X, 0) + 3
• Sell an ATM call with X2 = $ 60 at a premium or price of C2 = $ 3; Resultant gain / (loss) = - max (X - X1, 0) + C2 = - max (X - 60, 0) + 3
• And buy an OTM call with X3 = $ 70 at a premium or price of C3 = $ 0.20; Resultant gain / (loss) = max (X - X3, 0) - C3 = max (X - 70, 0) - 0.20

For stock price X, the gain / (loss) matrix from the iron butterfly will be:

= sum of the gain / (loss) from each of the four individual position above = max (50 - X, 0) - 0.30 - max (60 - X, 0) + 3 - max (X - 60, 0) + 3 + max (X - 70, 0) - 0.20 = 5.50 + max (50 - X, 0) - max (60 - X, 0) - max (X - 60, 0 ) + max (X - 70, 0)

So, please see the gain loss table and the graph subsequently:

X	Gain / Loss = 1.50 + max (50 - X, 0) - max (60 - X, 0) - max (X - 60, 0 ) + max (X - 70, 0)
35	-4.5
40	-4.5
45	-4.5
50	-4.5
55	0.5
60	5.5
65	0.5
70	-4.5
75	-4.5
80	-4.5
85	-4.5

Similarity between an Iron Butterfly and a Butterfly:

• Both are trading strategy to minimize losses
• Both are created using four options

Dissimilarity

• Iron Butterfly uses both call as well as put. Butterfly uses all call or all put at a time.