Actuarial Mathematics

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American option

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Actuarial Mathematics

Definition

An American option is a type of financial derivative that gives the holder the right to buy or sell an underlying asset at a specified strike price before or on its expiration date. This flexibility allows the holder to exercise the option at any time, making it a valuable tool for hedging and speculation in financial markets. American options can be used on various underlying assets, including stocks, commodities, and indices.

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5 Must Know Facts For Your Next Test

  1. American options can be exercised at any time up to their expiration date, while European options can only be exercised on the expiration date itself.
  2. This type of option is often more expensive than European options due to the added flexibility it provides to the holder.
  3. American options are commonly used in stock options trading, allowing investors to capitalize on short-term price movements.
  4. The ability to exercise American options early can be advantageous, especially when dividends are involved, as holders may want to capture those payments.
  5. The pricing of American options often involves more complex models, like binomial trees or numerical methods, due to their early exercise feature.

Review Questions

  • Compare and contrast American options with European options in terms of their exercise features and implications for investors.
    • American options allow holders to exercise their rights at any time before or on the expiration date, providing greater flexibility compared to European options, which can only be exercised at expiration. This difference means that American options may have higher premiums due to their early exercise feature. Investors might choose American options when they anticipate volatility or wish to take advantage of dividends that could influence the underlying asset's price.
  • Discuss how the early exercise feature of American options impacts their valuation compared to European options.
    • The early exercise feature of American options complicates their valuation because it introduces additional factors that must be considered, such as the potential for dividends and changing market conditions. Models like binomial trees are often employed to account for these factors and determine the option's fair value. In contrast, European options have simpler valuation models since they lack this flexibility, typically resulting in lower premiums compared to American options.
  • Evaluate the strategic advantages of holding an American option in a volatile market environment and how it may influence an investor's decision-making.
    • Holding an American option in a volatile market offers strategic advantages, such as the ability to capitalize on rapid price movements by exercising the option at optimal times. This flexibility allows investors to react quickly to market conditions and potential opportunities, such as exercising before significant price drops or capturing dividend payments. As a result, this adaptability can enhance returns and manage risk more effectively compared to relying solely on European options that limit exercise timing.

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