(PCP and butterfly spread) Recall from Chapter 17 that a butterfly is an options strategy built on four trades at one expiration date and three different strike prices. For call options, one option each at the high and low strike prices are bought, and two options at the middle strike price are sold.

Consider the following spreads:

• Butterfly composed of calls: Buy one ABC June $180 call for $20, sell two ABC June $200 calls each at $10, and buy one ABC June $220 call for $5.

• Butterfly composed of puts: Buy one ABC June $180 put, sell two ABC June $200 puts, and buy one ABC June $220 put.

Use put–call parity to show that the cost of a butterfly spread created from the calls is identical to the cost of the butterfly spread created from European puts.