The Basics of Path-Dependent Options: Definition, Types, and Examples

Summary: 

Path-dependent options are a special type of exotic options. Their payoff changes based on the past prices of the asset they're linked to. There are different types like Asian, barrier, look-back, and chooser options. In this blog, you'll get to know these options, see their different types, and learn why derivatives traders use them.

In the 1970s, two bright minds, Black and Scholes, introduced a formula that changed how we look at European options. These options are unique contracts that let you make a decision only when they expire. The value of this decision is tied to the final price of an asset, like a stock or an index. Black and Scholes believed that a stock's price moved randomly, and no one could predict its next move.

But some traders were not happy with this simple model. They wanted to take advantage of the whole journey of the asset’s price, not just its final price. So they created a new type of option that considered the history of the asset’s price. This type of exotic option is now called a path-dependent option. 

In this blog, we will explore what are path-dependent options, and its various types. 

Defining path-dependent options

Path-dependent options are a unique subset of what's termed exotic options. These options are sensitive to the history of an asset's price. Every price movement, whether it's a rise or a fall, throughout a specified time, plays a part in determining the option's value.

There are two main categories of path-dependent options, that are: 

1. Soft path-dependent option: This is a type of path-dependent option where the payoff is dependent on a single final event or outcome. It doesn't consider the entire history of the asset's price. Common options in this category are barrier options, look-back options, and chooser options.
2. Hard path-dependent option: Contrary to the soft path-dependent option, the payoff here is influenced by the entire trajectory of the asset's price over a specified period. It takes into account the full history, making it a path-dependent option with strong memory. A notable example of this type of option is the Asian option.

Types of path-dependent options 

The movement of an asset directly affects the option's payout and its structure. There are four main types of options based on this asset movement. Let's explore them. 

• Asian options: One of the earliest examples of a path-dependent option is the Asian option. These are also called as average-rate options because payoffs are based on the average price of the asset over a specified period of time. This structure is especially popular in the commodity and forex markets, where the averaging approach helps to hedge against consistent cash flows. We'll provide a detailed example later in this blog to illustrate how Asian options work and how they differ from standard options.

• Barrier options: Another early example of a path-dependent option is the barrier option. They activate or become void when the asset's price hits a specific mark, often referred to as "knock-in/out" options. The payout depends on whether the asset's price reaches a set 'barrier'. A knock-out option becomes worthless if the asset's price surpasses a certain point. Conversely, a knock-in option gains value once the asset hits that price. 

Let’s say you have a knock-out call option with a strike price of INR 100 and a barrier at INR 120, you'll earn the difference between its final price and INR 100. But if the price exceeds INR 120 before expiry, the option becomes worthless.

• Chooser options: A chooser option, also known as a double option, gives you the option to choose later whether you want a call or put option. You only make this decision on a certain date before the option expires. It is like having the right to pick the best option based on the market situation. 

Suppose you have a chooser option with a strike price of INR 1000, expiring on 31 December 2023. On 30 September 2023, you will look at the asset’s price. Depending on what you see, you will then select either a call or put option, keeping the original terms (strike price and expiration date).

• Look-back options: With a floating strike look-back option, the strike price is determined at expiration by the asset's best price during its term. For call options, it's the lowest price; for put options, the highest. Your profit is the difference between the final and strike price. Meanwhile, a fixed strike look-back option's price is set at the beginning.

For instance, if you have a floating strike look-back call option priced at INR 100 expiring on 30 September 2023, and the asset drops to INR 75 anytime before then, you can buy it at INR 75, regardless of its 30 September value. Your profit is the difference between the final and INR 75.

Example of path-dependent options 

Let’s understand how an Asian call option with a strike price of INR 500, set to expire on 15 November 2023 would work. In this example, the average price is determined using the arithmetic mean of the daily closing prices from the start of the year until 15 November 2023. The frequency of sampling is weekly, meaning that every Friday’s closing price is used to calculate the average.

Assume that the weekly closing prices from January 1 to November 15 are as follows:

The average price is then (480 + 490 + 500 + … + 520) / 45 = INR 505.56

The payoff of the Asian call option is the difference between the average price and the strike price, which is INR 505.56 - INR 500 = INR 5.56

If you had a standard call option with the same strike price and expiration date, your payoff would be based on the spot price on November 15, which is INR 520. Your payoff would be INR 520 - INR 500 = INR 20

As you can see, the Asian option has a lower payoff than the standard option in this case, because the average price is lower than the spot price. However, this also means that the Asian option has a lower premium than the standard option, because it has less volatility and risk. The Asian option can be more attractive if you expect the underlying asset to have a stable or declining price over time. 

Wrapping up: Key points to remember 

• Path-dependent options payoff is contingent on the asset’s price path, not just its final value.
• Some path-dependent options are traded on exchanges like the CME and Euronext Amsterdam. Others are traded privately (over-the-counter).
• Path-dependent options have low volume, which means less liquidity and higher costs than standard options.

Ready to start trading in derivatives or keen to learn more? Head over to our app now.