Lookback Options

A lookback option, also known as a hindsight option, is a type of exotic derivative contract that allows the investor to take advantage of the best price the underlying asset achieves over the life of the option. This article will provide definitions of the different forms of lookback options and explain how they work, as well as giving general information on their pricing and other matters of interest to traders.

What Is A Lookback Option?

Lookback options allow investors to review the historic price of the underlying asset while making their decision on whether to exercise their option. This allows the option buyer to avoid the regret of missing out on an ideal exit point that they may have neglected at the time, hence the moniker “hindsight option”.

However, this kind of flexibility comes at a price, and lookback options are expensive to set up, with investors paying a premium that could cancel out much or all of their profits.

Lookback call option definition

How Do Lookback Options Work?

A good way of understanding the meaning of lookback options is to compare this type of derivative to the standard or ‘vanilla’ call and put options.

A standard call option is a contract which gives the buyer the right, but not the obligation, to buy an asset such as a stock or commodity for an agreed price or “strike price” at any point within a specified time frame, such as 6 months.

Imagine an investor buys a call option on stock from the communications tech company Zoom in March 2020. When the contract is made, Zoom stock is valued at $100, and the agreement gives the contract buyer the right to purchase the stock at a strike price of $150 any time before the contract’s expiry date in December 2020.

Over the course of the year, Covid-19 lockdowns send Zoom stock skyrocketing to a peak above $550 in October before dropping to around $350 in December.

The contract buyer in this case would be one happy investor, having had the opportunity to make a tasty return on their investment by exercising their option at almost any point over that year. However, they may still experience regret if they exercised their option in June or December and thus missed the chance to make the maximum profit by doing so in October.

A lookback option effectively protects the contract buyer from that risk because it means they have the right to benefit from the point when the underlying asset’s price is most advantageous to them over the life of the option.

In the case of lookback options, payoffs depend on the path that the underlying asset’s price moves over the option’s life, so a lookback option is defined as “path-dependant”, and as it is more complex than standard option contracts, it is known as an exotic option.

As with other products of this type, lookback options are almost always tailor-made contracts sold over the counter, rather than on exchanges, and thus carry the risk that one side may default.

Lookback options are more expensive than their plain vanilla alternatives, but they are still considered useful by investors for hedging against volatility. They typically come in two main types:

  • Fixed strike
  • Floating strike

Fixed & Floating Strike Lookback Options

Since the path of the underlying asset’s value can fluctuate either way over the life of an option, the point of entry can be just as important as the exit point.

To illustrate how this works, first let’s imagine someone opens a short position on Zoom stock by opening a six-month put option when Zoom stock was at $450 in September 2020. The stock price rises to $550 in October, then falls to a low around $340 in January before climbing again to around $420 when the option expires in February.

Fixed Strike Lookback Option

In a fixed strike lookback option, the strike price is determined according to the value of the underlying asset at the time the option is purchased. When the fixed strike lookback option is exercised, the contract holder will obtain the most advantageous price over the life of the contract.

So, in the case of the Zoom put option, the payoff would be based on the difference between the strike price – let’s say $450 – and $340, the lowest price Zoom stock reach over the course of the contract.

In other words, the fixed strike allows the contract buyer to pick the most advantageous point to exit the option.

Floating Strike Lookback Option

Conversely, in a floating strike lookback option the strike price is automatically set to the optimal price throughout the life of the contract. In the case of our example, this would set the strike price at $550, the optimal entry point, and the payoff would be determined by the difference between this strike price and $420, the market price at maturity.

So, the floating strike option has provided the contract buyer with the optimal entry point.

Pricing Lookback Options

As we’ve seen, lookback options take away the uncertainty of choosing the right exit or entry point for an investment. So what are the drawbacks?

In short, lookback options come at a high price, and this often outweighs the potential benefits of this option for a contract buyer. The payoff of a lookback option is based on the price of the underlying asset over the life of the contract, so it is difficult to determine the price of the contract using analytic formulas.

Instead, the price of the contract can be determined in a number of ways:

  • Monte Carlo simulations are considered the most straightforward way to determine the price of a lookback option contract. A Monte Carlo simulation is used to predict the probability of outcomes when random variables are present, and can be used in a programme like Excel to create a forecasting model for lookback options.
  • Binomial tree models are also frequently used in pricing derivatives including lookback options. This method involves creating a model of the intrinsic values an option could take over varying time periods.
  • Computer programmes are also frequently used, including tools created in languages like Python, Matlab, C++ or Javascript. These tools can be used to create Monte Carlo simulations or binomial tree models, for example.

Finally, finance is ever a rich field for analysis, and more methods have been presented as having the potential to work as a lookback option pricer or calculator, including partial differential equations (PDE).

Discrete lookback options

Other Types Of Lookback Options

The term lookback option has become widely used in the United States as of 2022, thanks to a US government policy that allowed taxpayers to “look back” to the 2019 tax year when calculating the size of their 2020 tax credit. With that said, this has nothing to do with lookback options as derivatives.

Similarly, the term “lookback” is used in the context of US healthcare and Medicaid. Again, this is not to be confused with the function of the exotic derivative we have delved into in this guide.

Note, lookback options are unavailable at many retail trading brokers. For more information on trading options, see our comprehensive guide.

FAQ

What Is A Lookback Option?

A lookback option is a type of exotic derivative that allows the contract buyer to obtain the optimal price for a particular security over the period of the contract. Find out how to apply a financial valuation for lookback options using our guide.

What Is The Value Of Lookback Options?

Lookback options provide value to investors as they allow them to hedge against price volatility and remove the uncertainty over when to exercise an option. The value of a lookback option’s payoff depends on the difference between the strike price and the market value when the contract matures.

Can You Buy Lookback Options On Exchanges?

Lookback options are exotic derivatives, which are almost always tailor-made and sold over the counter, and not on exchanges.

How Are Lookback Options Priced?

Lookback options can be priced by several methods, including Montecarlo simulations and binomial tree models. See our guide above for details on popular mechanisms.