Trading Strategies (Butterfly Spread) – Solved Example

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LOS: Describe the use and calculate the payoffs of various spread strategies.

Question:

Tabulated below are premiums of various European calls, all having the same underlying and expiration (calculated assuming $r_f=7.80\%$):

OptionExpiryStrikePremium
Call6-months\$30\$5.23
Call6-months\$33\$3.72
Call6-months\$36\$2.58

If you were to create a 6-month, 30-33-36 butterfly spread using put options of strikes \$30, \$33 and \$36, at what final stock price(s) ($𝑆_𝑇$) will the strategy break even? Ignore time value of money in calculating your profit.

A.At $𝑆_𝑇=35.63$.
B.At $𝑆_𝑇=30.37$ and at $𝑆_𝑇=35.63$.
C.At $𝑆_𝑇=29.63$ and at $𝑆_𝑇=36.37$.
D.At $𝑆_𝑇=36.37$.