American options

Definition

American options are a type of financial derivative that allows the holder to buy or sell an underlying asset at a predetermined price, known as the strike price, at any time before or on the expiration date. This flexibility gives American options a distinct advantage over European options, which can only be exercised at expiration. The valuation of American options is particularly complex because their early exercise feature needs to be accounted for, especially in jump diffusion processes.

5 Must Know Facts For Your Next Test

1. American options can be exercised at any point up to and including their expiration date, making them more flexible compared to European options.
2. The ability to exercise American options early can lead to different pricing strategies and valuation methods due to the need to consider the optimal exercise strategy.
3. In jump diffusion processes, American options' values can be significantly affected by sudden jumps in asset prices, necessitating numerical methods for accurate pricing.
4. Common numerical methods for valuing American options include binomial trees and finite difference methods, which help in determining the optimal exercise strategy.
5. The early exercise premium is the additional value associated with the ability to exercise American options before expiration, which is important when considering dividends or sudden market shifts.

Review Questions

• How does the flexibility of American options influence their valuation compared to European options?
  • The flexibility of American options allows holders to exercise them at any time before expiration, which adds complexity to their valuation. This is because valuing American options requires considering multiple possible exercise points and the potential benefits of early exercise. In contrast, European options are simpler to value since they can only be exercised at expiration, resulting in fewer factors affecting their price.
• Discuss how jump diffusion processes impact the pricing strategies for American options.
  • Jump diffusion processes introduce significant price changes alongside normal market fluctuations, affecting how American options are priced. These jumps can create scenarios where it is advantageous for option holders to exercise their rights early due to anticipated market movements. As a result, pricing strategies must incorporate numerical methods that account for both the regular price path and potential jumps, ensuring accurate valuations that reflect the unique risks associated with American options.
• Evaluate the implications of using numerical methods for valuing American options in jump diffusion models.
  • Using numerical methods to value American options within jump diffusion models allows for a more nuanced understanding of how unexpected price changes affect option pricing. These methods, such as binomial trees or finite difference approaches, enable analysts to simulate various scenarios and determine optimal exercise strategies. By incorporating both continuous movements and discrete jumps in asset prices, these models provide a comprehensive framework for pricing that captures the complexities inherent in American options and aids investors in making informed decisions.

Related terms

European options: A type of option that can only be exercised at its expiration date, lacking the flexibility that American options offer.

Jump diffusion process: A mathematical model that accounts for sudden, large changes in the price of an asset, along with continuous price movements, often used in the pricing of derivatives.

Black-Scholes model: A mathematical model used for pricing options by determining the theoretical value based on factors like the underlying asset's price, volatility, time to expiration, and risk-free interest rate.