Project 8 Option Strategy Reverse Engineering
Project 8 Option Strategy Reverse Engineering
This project involves reverse engineering an option strategy based on a specified portfolio payoff diagram. The goal is to determine the combination of financial instruments—stocks, calls, and puts—that replicate the given payoff profile. Additionally, the project requires calculating the total cost of this portfolio and visualizing its payoff diagram using Excel.
Paper For Above instruction
Reverse engineering an option strategy involves systematically deducing the combination of financial instruments that produce a desired payoff profile at maturity. The process starts with analyzing the provided payoff diagram, understanding its structure, and then constructing a portfolio that mirrors this profile as closely as possible. In this particular case, the client desires a specific payoff diagram with all slopes having an absolute value of 1, which suggests a linear payoff structure with certain slopes at different stock price levels.
The given scenario involves a stock currently priced at $10, alongside several options with specified strike prices and premiums. The available options span strike prices from $20 to $100, with both calls and puts offered at varied premiums. To replicate the specified payoff diagram, it is essential to consider a combination of buying and writing these options along with the underlying stock.
Understanding the Payoff Diagram
The target payoff diagram exhibits linear segments with slopes of either +1 or -1, indicating a strategy that involves creating a payoff that changes linearly with stock price in different regions. Typically, such diagrams are associated with strategies like spreads, straddles, or combinations thereof, constructed via purchasing or writing options at various strike prices to produce a piecewise linear payoff profile.
How to Obtain the Payoff Diagram
The key to obtaining the payoff diagram is to identify a combination of options and stock positions that produce the desired slopes across various stock price levels. For example, a long stock position provides a slope of +1 (since payoff increases dollar-for-dollar as stock price rises). Conversely, a short call position at a specific strike introduces a slope of -1 beyond that strike, as the writer of a call loses unlimited upside potential.
By combining long or short positions in multiple call and put options with different strikes, along with the underlying stock, one can achieve a piecewise linear payoff with the specified slopes. For instance, buying a stock and writing a call at a certain strike creates a "covered call" payoff, which has a flat region beyond the strike and an upward slope below it. Conversely, buying a put adds a protective downside, shaping the payoff profile accordingly.
Constructing the Specific Portfolio
Based on the options and premiums provided, the construction involves selecting the appropriate options to create the segments with slopes of ±1 at the specific strike prices. For example, the segment from below $20 might involve owning the stock, while the segments between strikes might involve combinations like a bull call spread, bear put spread, or other composite strategies. Details of the exact combination can be derived by analyzing the slopes and aligning them with the premiums to ensure the resulting payoff closely matches the target diagram.
Calculating the Cost
The total cost of the portfolio is obtained by summing the prices of all purchased instruments and subtracting premiums received from written options. For each selected option and stock position, multiply the quantity by its premium or current price and sum these to determine the initial investment. This cost assessment helps ensure that the strategy is feasible within the client’s budget.
Visualizing the Payoff in Excel
To visualize the payoff profile, use Excel by setting a range of stock prices along the x-axis. For each stock price point, calculate the total payoff from the combination of stock and options using the respective payoffs at that price. Plot these values using a scatter plot with straight lines to obtain a clear graphical representation of the strategy’s payoff structure. Such visualization aids in verifying whether the constructed portfolio aligns with the desired payoff profile.
Conclusion
Reverse engineering an option strategy requires understanding the linear segments and their slopes, then constructing a portfolio of stocks, calls, and puts to replicate this structure. By accurately selecting options at different strikes and combining them with stock holdings, it is possible to produce a payoff diagram with the specified characteristics. Calculating the initial cost and visualizing the payoff in Excel completes the process, providing a comprehensive understanding of the engineered strategy.
References
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