Chapter 10: Problem 19
Three put options on a stock have the same expiration date and strike prices of \(\$ 55, \$ 60\), and \(\$ 65\). The market prices are \(\$ 3, \$ 5\), 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?
Short Answer
Step by step solution
Understanding Butterfly Spread
Calculating Initial Investment
Analyzing Profit or Loss at Expiration
Constructing the Payoff Table
Determine Range for Loss
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Put Options: The Basics
When you purchase a put option, you're paying for insurance; if the stock price drops below the strike price, you can sell your shares at this predetermined level, effectively protecting yourself from further loss.
- **Right to Sell**: You have the option to sell, not an obligation.
- **Strike Price**: Predetermined price at which you can sell the stock.
- **Expiration Date**: The period within which you can exercise the option.
In a butterfly spread, put options are strategically used at different strike prices to take advantage of minimal stock movement.
Understanding Strike Price
In creating a butterfly spread with put options, different strike prices are used to construct a specific payoff profile. For example:
- Buying one put option at a low strike price (e.g., $55).
- Selling two put options at a middle strike price (e.g., $60).
- Buying another put option at a high strike price (e.g., $65).
Exploring Option Strategies: Butterfly Spread
With a butterfly spread, you are:
- Gaining exposure to price stability with limited risk.
- Buying and selling put options at different strike prices.
- Limiting potential profit to manage risk and cost.
Creating a Payoff Table
For the butterfly spread using put options, the payoff table will show how each combination of stock price and option action (buy/sell) will impact the total profit or loss:
- Below the lowest strike price, a profit is made.
- At the middle strike price, the maximum loss is incurred if the options expire worthless.
- Above the highest strike price, losses are capped as long as the options remain unexercised.