This toolkit allows users to explore various scenarios for option pricing by adjusting key parameters. It supports different option types, including Plain Vanilla, Lookback, and Restricted Quantile Lookback options, providing flexibility for various financial strategies.
Important Note: The following relationship must hold at any time t:
Minimum Price ≤ Stock Price ≤ Maximum Price
Ensuring this constraint is crucial for accurate calculations, especially for Lookback and Quantile Lookback options.With this toolkit, traders and financial analysts can visualize how these parameters influence the value of options, offering an indicative view of the market. However, users are advised that decisions made using this toolkit are at their own risk, as the toolkit is intended for educational and exploratory purposes and does not guarantee market outcomes.
Enter data and click "Calculate" to see results here.
In addition to the What-If Analysis Toolkit, you can explore the Option Trading Strategies Toolkit. This tool provides option values (prices), payoff, profit/loss, and Greeks (Delta, Gamma, Vega, Theta, and Rho) for European-style plain vanilla options across the following asset types: stocks, currency (Fx) spot or forward, and currency (Fx) futures. Visit www.optionstrategiescalculator.com to learn more.
This study investigates the relationships between European-style Plain Vanilla, Lookback, and Quantile Lookback Options. It introduces a "what-if" analysis toolkit based on closed-form analytical solutions for these options, helping analysts and practitioners better understand their hedging capabilities and speculative potential.
Currently, the toolkit supports European-style options, which can only be exercised at maturity. American-style options, which allow exercise at or before maturity, are not yet supported.
Plain Vanilla Options are fundamental derivatives offering the right, but not the obligation, to buy or sell the underlying asset at a predetermined strike price at maturity. While simple and cost-effective, they depend solely on the terminal price of the asset.
Lookback Options allow the holder to optimize their payoff by referencing the maximum or minimum price of the asset during the option's lifetime. However, this flexibility results in higher premiums. Lookback options are typically more expensive than Plain Vanilla options because they provide the holder with an optimal payoff scenario.
To address the cost challenge, Quantile Lookback Options have been introduced. Instead of using the absolute maximum or minimum price of the underlying asset, the payoff of these options depends on a specific quantile of the price history. By relaxing the reliance on extreme price levels, quantile-based lookback options offer a more affordable alternative, while still capturing favorable price movements to a significant degree. This adjustment reduces premiums while retaining significant sensitivity to favorable price movements. Despite their cost-effectiveness, these options are computationally complex due to their reliance on the entire price history, introducing path dependency and non-Markovian behavior.
To simplify this complexity, we propose the Restricted Quantile Lookback Option, which limits the price history considered to a subset relative to the current price. This restriction reduces computational demands while maintaining the essential characteristics of quantile-based options. By leveraging the closed-form solutions of standard Lookback Options, we derive a tractable closed-form solution for the restricted quantile lookback option, establishing a direct relationship between them. This framework highlights how quantile-based adjustments effectively balance cost and payoff. For detailed derivations and formulas used in the toolkit, see references: