Adjusted average option: Meaning, Criticisms & Real-World Uses

What Is an Adjusted Average Option?

An Adjusted Average Option, often referred to simply as an Asian option, is a type of option contract whose payoff depends on the average price of its underlying asset over a specified period, rather than the price at a single point in time, such as the expiration date. This characteristic places the Adjusted Average Option within the broader category of financial derivatives, specifically as a form of exotic options. Unlike standard European or American options, which rely on the spot price at maturity, the averaging mechanism of an Adjusted Average Option helps reduce the impact of extreme price fluctuations at the time of exercise. This feature can make them less susceptible to market manipulation at maturity and may lead to lower premiums compared to traditional options due to reduced volatility of the average price²⁸, ²⁹.

History and Origin

The concept of options trading has roots stretching back to ancient Greece, with philosophical anecdotes predating modern financial markets²⁶, ²⁷. However, the formalization and exchange-traded standardization of options are a much more recent development. The modern options market gained significant traction with the establishment of the Chicago Board Options Exchange (CBOE) in 1973, which introduced standardized option contracts and a centralized clearinghouse²⁵. The first commercially used pricing formula for options linked to the average price of crude oil, leading to the coining of the term "Asian option," was developed in Tokyo in 1987 by Mark Standish and David Spaughton of Bankers Trust. These "average options" or Adjusted Average Options emerged to address specific business needs, particularly in commodity markets where exposure to price fluctuations occurs over a period, rather than at a single point²⁴.

Key Takeaways

An Adjusted Average Option is a type of option contract whose payoff is based on the average price of its underlying asset over a predetermined period.
It is considered an exotic option due to its path-dependent nature, differing from standard options that use the spot price at expiration.
The averaging mechanism helps reduce the impact of short-term price spikes or manipulation at maturity, leading to potentially lower volatility and premiums.
Adjusted Average Options can be either "average price" options (with a fixed strike price) or "average strike" options (where the average becomes the strike)²³.
They are particularly useful for hedging continuous exposures to an asset's price, common in commodity and currency markets.

Formula and Calculation

The valuation of an Adjusted Average Option can be complex, especially for arithmetic averages, as there is typically no simple closed-form analytical solution like the Black-Scholes model for standard European options²¹, ²². The average can be calculated in various ways, most commonly as an arithmetic mean or a geometric mean of the underlying asset's price over discrete intervals.

For an arithmetic average call option, the payoff at expiration date (T) is:

\text{Payoff} = \max\left( \frac{1}{N} \sum_{i=1}^{N} S_i - K, 0 \right)

And for an arithmetic average put option, the payoff is:

\text{Payoff} = \max\left( K - \frac{1}{N} \sum_{i=1}^{N} S_i, 0 \right)

Where:

( S_i ) = The underlying asset's price at observation point (i)
( N ) = The total number of observation points over the averaging period
( K ) = The strike price (for average price options)

While geometric average Asian options have analytical solutions, arithmetic average options often require numerical methods for pricing, such as Monte Carlo simulation or finite difference models, to approximate their value¹⁹, ²⁰. Academic research continues to explore methods for computing their price accurately¹⁷, ¹⁸.

Interpreting the Adjusted Average Option

An Adjusted Average Option is interpreted by understanding its core function: to smooth out price volatility over time. This makes them particularly attractive for participants who have ongoing exposure to an underlying asset and are more concerned with the average cost or revenue over a period rather than a single point in time. For instance, a manufacturing company that regularly purchases a commodity might prefer an Adjusted Average Option to hedge against the average cost of that commodity over a quarter, rather than a single purchase price.

The payoff of an Adjusted Average Option is typically less volatile than a standard option because the averaging process reduces the impact of any extreme price movements. This dampening effect means that while they offer less upside potential in rapidly rising or falling markets, they also present less downside risk from sudden adverse price spikes near the expiration date.

Hypothetical Example

Consider a hypothetical company, "Global Grains Inc.," which regularly buys wheat for its food production. To manage its input costs, Global Grains decides to purchase an Adjusted Average Option (specifically, an average price call option) on wheat.

Scenario:

Underlying Asset: Wheat futures contract
Strike Price ((K)): $6.00 per bushel
Expiration Date: 3 months from now
Averaging Period: Weekly observations for the last month before expiration (4 observations)

Observation Prices:

Week 1 (2 months, 3 weeks out): $6.10
Week 2 (2 months, 2 weeks out): $5.90
Week 3 (2 months, 1 week out): $6.30
Week 4 (at expiration): $6.50

Calculation of Average Price:
The average price of wheat over the last month would be:

\text{Average Price} = \frac{(\$6.10 + \$5.90 + \$6.30 + \$6.50)}{4} = \frac{\$24.80}{4} = \$6.20

Payoff Calculation:
The payoff for Global Grains Inc. at expiration date would be:

\text{Payoff} = \max(\text{Average Price} - \text{Strike Price}, 0)

\text{Payoff} = \max(\$6.20 - \$6.00, 0) = \max(\$0.20, 0) = \$0.20 \text{ per bushel}

In this example, Global Grains Inc. would profit $0.20 per bushel from the Adjusted Average Option because the average wheat price ($6.20) was above their strike price ($6.00). This helps them offset a portion of their higher purchasing costs in the open market due to the rising wheat prices over the period.

Practical Applications

Adjusted Average Options find practical applications in several areas, particularly where consistent price exposure or protection against market manipulation is desired:

Commodity Markets: Industries that consume or produce large quantities of commodities (e.g., oil, agricultural products, metals) can use these options to hedge against the average price over a production cycle or consumption period, providing more stable cost or revenue projections¹⁶.
Foreign Exchange: Businesses engaged in international trade can use Adjusted Average Options to manage currency risk management over a transaction's duration, protecting against unfavorable average exchange rates.
Risk Management: For large-scale projects or long-term contracts where a single, instantaneous price observation might be vulnerable to manipulation or unusual market events, an Adjusted Average Option offers a more robust hedging instrument.
Derivatives Market: These derivatives are part of the broader over-the-counter (OTC) derivatives market, where customized contracts are common. Regulators, such as the Federal Reserve, monitor this market due to its systemic relevance and interconnectedness within the financial system, emphasizing the need for transparency and appropriate risk management ¹⁴, ¹⁵.

Limitations and Criticisms

While Adjusted Average Options offer distinct advantages, they also come with limitations and criticisms:

Complexity: The primary drawback is their increased complexity compared to standard European option or American option contracts. Their valuation requires more sophisticated mathematical models, such as Monte Carlo simulations, as closed-form solutions for arithmetic averages are not available¹², ¹³. This complexity can make them harder for less experienced investors to understand and price accurately.
Liquidity: As exotic options, Adjusted Average Options are primarily traded in the over-the-counter (OTC) market, meaning they may have lower liquidity compared to exchange-traded options¹¹. This can make it challenging to enter or exit positions quickly without impacting prices.
Reduced Leverage: The averaging mechanism, while reducing volatility, also inherently reduces the potential for high leverage and large payoffs that can be seen with standard options based on a single spot price observation. This is a trade-off for the added stability.
Tail Risk Exposure: While averaging reduces general volatility, specific market conditions can still expose these options to significant tail risk. Unexpected sustained movements in the underlying asset price can still lead to substantial losses.
Regulatory Scrutiny: The complexity of derivatives, including Adjusted Average Options, has drawn increased regulatory scrutiny, particularly after financial crises highlighted risks in the OTC derivatives market. Regulators aim to enhance transparency and reduce systemic risk through reforms¹⁰.

Adjusted Average Option vs. Adjusted Option

The term "Adjusted Average Option" (or Asian option) refers to a financial instrument whose payoff mechanism itself is based on an average price. It is a specific type of option contract designed with an averaging feature.

In contrast, an "Adjusted Option" refers to an existing, standard option contract whose terms (such as the strike price, deliverable, or contract multiplier) have been modified by the Options Clearing Corporation (OCC) due to a corporate action affecting the underlying asset⁸, ⁹. Examples of such corporate actions include a stock split, reverse stock split, merger, acquisition, or special dividend ⁶, ⁷. The purpose of adjusting an option is to ensure that the economic value and obligation of the contract remain largely unchanged for the holder despite the changes to the underlying security⁴, ⁵. Therefore, while an "Adjusted Average Option" is a distinct product, an "Adjusted Option" is a standard option that has undergone a modification.

FAQs

What is the main benefit of an Adjusted Average Option?

The main benefit of an Adjusted Average Option is its ability to reduce the impact of volatility and potential price manipulation at a single point in time. By using an average price over a period, it provides a smoother, more stable payoff, which can be beneficial for hedging continuous exposures.

Are Adjusted Average Options common?

Adjusted Average Options are considered exotic options and are less common than standard European option or American option contracts. They are primarily traded in the over-the-counter (OTC) market and are often customized to meet specific needs of institutional investors or corporations, particularly in commodity and foreign exchange markets³.

How do you price an Adjusted Average Option?

Pricing an Adjusted Average Option, especially one based on an arithmetic average, is more complex than pricing standard options. Since there isn't a simple, widely accepted analytical formula, numerical methods like Monte Carlo simulation or finite difference models are typically used to estimate their value¹, ². This involves simulating many possible price paths for the underlying asset and averaging the resulting payoffs.