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

Please refer to the explanation section

Explanation:

Put - Call parity defines the relationship that exists between  European puts options and European Call options, in terms of the Put-Call Parity Relationship holding a short European Put Option and a long European call Option at the same time will generate the same return as holding a Forward Contract on the same underlying assets when expiration period is is the same and forward price equals strike price.

suppose we buy a European call option for ABC Corporation's stock. The call option expires in a year from now.  The strike price is $30, and buying  the call option costs $10.

This Call option gives us the right but not the obligation to buy the stock of ABC Corporation in a year from now (expiry date)for $30. Regardless of what the market price might be. If one year from now, ABC corporation's stock is trading at $20, we will not exercise the option. When the stock of ABC Corporation is trading at $40 per share, We will exercise the option. When the Share price is $40 we will break even ($30 dollar + $10 cost = $40). We will make profit on  Any amount  above $40

suppose we also decide to write a European put option for ABC Corporation's stock with the same expiration date, strike price, and cost of the option. We receive $10 from writing the option.

The buyer has purchased the right, but not the obligation, to sell us ABC Corporation's  stock at the strike price of $30 and we are  are obligated to take that deal, regardless of what ABC Corporation's market share price might be.

If ABC Corporations stock is trading at $20 a year from now, the buyer will sell us the stock at $30 and we will break even and also the buyer will break even.  We already received $10 from selling the Put Option plus Share Price of $ equals $30. If stock of ABC Corporation is trading at $30 or above, we will make a profit of $10  because the buyer will not exercise the Put Option.

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