Three put options on a stock have the same expiration date...

Three put options on a stock have the same expiration date and strike prices of $\$ 55, \$ 60$ and $\$ 65 .$ The market prices are \$ 3,55,$ and $\$ 8,$ respectively. Explain how a butterfly spread can be created, Construct a table showing the profit from the strategy. For what range of stock prices would the butterfly spread lead to a loss?

Key Concepts

Butterfly Spread

A butterfly spread is an options strategy that involves taking positions on three different strike prices, usually by buying options at the lower and higher strikes and selling twice as many options at the middle strike. This structure creates a 'tent-shaped' profit profile where maximum profit is achieved if the underlying asset’s price remains near the middle strike at expiration, with limited risk if the price moves significantly away from this level.

Put Options

Put options give the holder the right, but not the obligation, to sell the underlying asset at a specified strike price before or at expiration. They are commonly used in strategies like the butterfly spread to benefit from or hedge against decreases in the underlying asset's price, or to structure a risk/reward profile with defined losses and gains.

Options Premium

The options premium is the price paid to acquire an options contract. In multi-leg strategies such as the butterfly spread, each leg has its own premium, and the net cost (or credit) of the strategy is determined by the combination of buying and selling these premiums. This net cost is important in determining the overall profit and loss of the strategy.

Profit and Loss Table

Constructing a profit and loss table involves calculating the payoff for each component of the option strategy across a range of final underlying prices at expiration, and then summing these to determine the overall profit or loss. This table helps visualize how the strategy performs under different market conditions and identifies the price ranges where the strategy is profitable or incurs a loss.

Breakeven Analysis

Breakeven analysis in the context of options strategies involves determining the underlying asset prices at which the net profit of the strategy is zero. For a butterfly spread, this analysis helps identify the price range where the trader starts to lose money, typically occurring when the underlying price moves sufficiently away from the middle strike, thereby reducing the value of the winner legs relative to the cost incurred.

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