Question

A one-month European call option on Bitcoin is with the strike price of $8,505, $8,705, and $8,905 are trading at $600, $500, and $415, respectively. An investor implements a butterfly spread (i.e., she buys one call with the strike price of $8,505, sells two calls with the strike price of $8,705, and buys one call with the strike price of $8,905. If at the maturity, the Bitcoin price is $8,605, what is the investor's profit?

Answer 1

You need to pay money when you buy option and you get money when you sell option.

So the Intial Inflow/Outflow of investor from the Postion =  - Outflow from buying one call with the strike price of $8,505 + Inflow from selling two calls with the strike price of $8,705 - Outflow from buying one call with the strike price of $8,905

= - 600 + (500) * 2 - 415

= -15

So investor incurred an outflow of $15 at the beginning of the strategy. As it is call option, so investor will earn from long call if bitcoin price increases, on the other hand he will lose from short call if bitcoin price increases.

Effects on each call option with change in Bitcoin Price to $8,605

- Effect in Long Call with Strike $8,505. As Bitcoin price increased, so there is profit in long call

Profit = Bitcoin Price - Strike Price

= 8,905 - 8,505

= 400 (So profit)

- Effect on 2 short calls with strike of 8,705. As Bitcoin price crosses the strike price, so loss on short call

= Number of calls * (Bitcoin Price - Strike Price)

= 2 * (8,905 - 8,705)

= 2 * 200

= 400 (So loss)

- Effect on long call at strike $8,905, as the Bitcoin price is same as strike price, so no loss and no profit.

Now combining all 4 options. The net profit / loss

= 400 - 400 + 0

= 0

From the butterfly spread, investor didn't earn any profit or loss. As the investor spent $15 on entering the strategy. So that is his total loss.

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