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Bermuda option (derivative)

Categoria — Derivati
By Azat Alymov, North America Group of Cbonds
Updated June 25, 2024

What is a Bermuda Option?

A Bermuda option is a unique type of exotic options contract that offers a middle ground between American and European options. Unlike American options, which provide the flexibility to exercise at any time before expiration, Bermuda options come with predetermined exercise dates. These exercise dates are typically spread out, occurring on specific dates, often one day each month/quarter/half-year/year. This feature sets Bermuda options apart from their European counterparts, which only allow exercise at the option's expiration date.

Bermuda options enable investors to either purchase or sell a security or underlying asset at a preset price on these specified exercise dates, as well as on the option's expiration date. This particular exercise schedule grants more control to investors than European options, which have a single exercise date, but less flexibility compared to American options.

In essence, Bermuda options offer a unique combination of predetermined exercise dates, granting investors the opportunity to manage their investments and hedge their positions at certain dates, providing a level of control in their options trading strategies.

Bermuda Option

Advantages and Disadvantages


  1. Lower Premiums. Bermuda options often come with lower premiums compared to American options. This can be an attractive feature for investors looking to gain exposure to an asset without incurring the higher cost associated with American options.
  2. Flexible Exercise Dates. One of the most significant advantages of Bermuda options is their flexibility when it comes to exercise. Investors can exercise the option on specific dates before the option's expiration. This level of control can be highly beneficial for those who want to align their investment strategies with market conditions.


  1. Higher Premiums than European Options. While Bermuda options offer lower premiums compared to American options, they are typically more expensive than European options. This cost difference may deter some investors who prefer the lower upfront expense of European options.
  2. Timing Uncertainty. The early exercise feature of Bermuda options, while providing flexibility, doesn't guarantee that exercising on the predetermined dates will be the most advantageous decision. The optimal exercise timing can be challenging to predict, and there's a risk that the chosen date may not align with favorable market conditions.

Pricing of Bermuda Options

The pricing of Bermudan options presents several challenges, primarily due to the multiple exercise dates associated with these options. In this aspect, Bermudan options share similarities with American options, which also involve pricing complexities compared to European options. To determine the value of Bermudan options, various techniques are employed.

One widely used approach to value Bermudan options is the Binomial Tree method. Another effective method is employing a Monte-Carlo framework. However, the Monte Carlo approach for Bermudan options differs from the traditional method, as it focuses on optimizing the exercise strategy. Analysts have several avenues to explore when utilizing Monte Carlo simulations for evaluating Bermudan options.

A specific approach to pricing Bermudan options is the dynamic programming approach. In this method, the option value for each predefined exercise date is determined as the maximum of the immediate exercise payoff, referred to as the intrinsic value. It also involves the challenging task of calculating the continuation value, which adds an extra layer of complexity to the pricing process.

Overall, the pricing of Bermudan options necessitates specialized techniques and methodologies, given the unique nature of these options and their exercise schedules. Analysts and investors often turn to approaches like the Binomial Tree and Monte Carlo simulations to accurately evaluate the value of Bermudan options.

American vs European vs Bermudan Options

The main differences between American, European, and Bermudan options lie in their accessibility and the degree of freedom they offer to investors. These differences primarily revolve around when and how you can exercise these options.

American Option

  • Premium. American options typically come with a higher premium due to their flexibility.
  • Exercisability. They can be exercised on any trading day between the purchase date and the option's expiration, offering maximum flexibility.
  • Liquidity. American options are the most liquid as they are traded on exchanges, making it relatively easier to exit or sell the contract.

European Option

  • Premium. European options usually have lower premiums compared to American options.
  • Exercisability. They can only be exercised on the option's expiration date, providing less flexibility compared to American options.
  • Liquidity. European options have medium liquidity and are typically traded over-the-counter (OTC).

Bermuda Option

  • Premium. The premium for Bermudan options is variable, falling between the higher premium of American options and the lower premium of European options.
  • Exercisability. Bermudan options allow exercise on predetermined dates specified in the contract, providing a middle ground between American and European options.
  • Liquidity. Bermudan options are often the most illiquid among the three, as they can be traded both over-the-counter (OTC) and fall into the category of exotic options.

Example of a Bermuda Option

Imagine an investor who owns shares of Apple Inc. They originally purchased the Apple stock at a price of $250  $215 per share and are concerned about the potential for a drop in the company's stock price.

To hedge against this risk, the investor decides to purchase a Bermuda-style put option. This put option has a six-month expiration period and a strike price of $210. The cost of the option is $3, or $300 since each option contract represents 100 shares of the underlying asset. This put option serves as insurance, protecting the investor's position from a decline in the stock price below the $210 strike price for the next six months. However, what makes it a Bermuda option is the flexibility it offers for early exercise on specific dates.

As the stock price of Apple falls to $180, the investor decides to take an action on the first day of the option's fourth month. They exercise the put option, effectively selling their stock position at the strike price of $210. This move results in a profit of $30 ($210 strike price - $180 stock price). However, this gain needs to offset the cost of the premium, which was $300, and any additional broker commissions incurred during the trading process.

It's important to note that the Bermuda feature in this option allows for early exercise on the first of each month starting from the fourth month. This flexibility provides the investor with the opportunity to protect their position as the stock price declines, mitigating potential losses.

On the other hand, if the stock price were to rise significantly, reaching $300 by the option's expiration, the investor would miss out on those gains. While Bermuda options offer the advantage of exercising early, it doesn't necessarily guarantee that exercising on specific dates will always result in optimal outcomes. Investors need to carefully consider their investment strategies and market conditions when utilizing Bermuda options.

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