Absolute variance swap

What Is Absolute Variance Swap?

An Absolute Variance Swap is a conceptual financial derivative that aims to provide exposure to the magnitude of an underlying asset's price movements, emphasizing absolute deviations rather than solely squared deviations as in traditional variance swaps. While the term "Absolute Variance Swap" is not as commonly standardized in financial markets as a variance swap or an absolute volatility swap, it conceptually falls under the broader category of volatility derivatives within financial derivatives. Unlike a conventional variance swap, which pays out based on the difference between realized variance (the square of volatility) and a predetermined strike price, an Absolute Variance Swap would theoretically focus on a measure of dispersion that incorporates the absolute value of price changes in its payoff mechanism or calculation of the underlying variance metric.

History and Origin

The concept of derivatives designed to trade or hedge against market volatility gained prominence in the late 1990s with the rise of variance swaps. These instruments emerged as a more direct way for investors to take a pure view on volatility without the directional exposure of traditional option contracts. However, standard variance swaps are convex in volatility, meaning their payoff accelerates as volatility increases, which can expose sellers to potentially unlimited losses.

In response to certain market demands and limitations of standard variance swaps, particularly regarding their convexity and the risks associated with extreme price movements, alternative volatility products were explored. For instance, JP Morgan launched the "absolute volatility swap" in May 2009, specifically designed to address these concerns. This instrument, which traded on major equity indices like the Dow Jones Euro Stoxx 50 and the S&P 500, paid out the difference between absolute realized volatility and a pre-agreed absolute volatility strike.¹⁸ This innovation aimed to offer better liquidity and transparency in challenging market conditions by removing some of the extreme risks associated with the convexity of variance.¹⁷ While "Absolute Variance Swap" is less defined, its conceptual underpinnings are likely rooted in similar attempts to refine volatility exposure through derivatives that incorporate absolute values.

Key Takeaways

• An Absolute Variance Swap is a conceptual derivative focused on the magnitude of price movements, distinct from a standard variance swap primarily by its "absolute" characteristic.
• It is designed to offer exposure to market dispersion, potentially by incorporating absolute price changes in its calculation or payoff.
• The term may be less standardized than "variance swap" or "absolute volatility swap."
• Its conceptual design likely aims to address specific market needs or limitations associated with the inherent convexity of traditional variance swaps.
• Such instruments could be utilized for specialized risk management or speculative strategies on volatility.

Interpreting the Absolute Variance Swap

Interpreting an Absolute Variance Swap would largely depend on its precise contractual definition, but generally, it would involve analyzing the relationship between the agreed-upon absolute variance strike and the actual realized variance (or a similar absolute-based measure of dispersion) over the contract's life. If the realized measure of absolute dispersion exceeds the strike, the holder of a long Absolute Variance Swap position would profit, while the counterparty would incur a loss. Conversely, if the realized measure is below the strike, the long position would lose value.

The interpretation would differ from a standard variance swap in how extreme price movements impact the payoff. Because the "absolute" nature might smooth out the effect of large squared deviations, an Absolute Variance Swap could be seen as offering a more linear exposure to volatility compared to the non-linear, convex payoff of a pure variance swap. This could make it appealing to market participants looking for a less volatile or more predictable volatility exposure. Effective interpretation requires a clear understanding of the underlying asset's price behavior and the specific methodology used to calculate the "absolute variance."

Hypothetical Example

Imagine an investor, Alpha, believes that the XYZ Index, currently trading at 1,000, will experience significant price fluctuations over the next three months, but wishes to avoid the extreme convexity inherent in a traditional variance swap. Alpha enters into a hypothetical Absolute Variance Swap with a counterparty, Beta.

The terms are:

• Underlying Asset: XYZ Index
• Maturity: 3 months
• Absolute Variance Strike: 250 (representing a conceptual annualized absolute variance measure)
• Notional Amount: $100 per absolute variance unit

Over the next three months, the XYZ Index moves up and down. At maturity, the realized "absolute variance" for the XYZ Index, calculated according to the specific terms of this hypothetical swap (e.g., based on the average of squared absolute daily log returns), is determined to be 300.

The payoff of the Absolute Variance Swap would be calculated as:
(\text{Payoff} = \text{Notional Amount} \times (\text{Realized Absolute Variance} - \text{Absolute Variance Strike}))
(\text{Payoff} = $100 \times (300 - 250))
(\text{Payoff} = $100 \times 50)
(\text{Payoff} = $5,000)

In this scenario, since the realized absolute variance (300) exceeded the absolute variance strike (250), Alpha, the buyer of the Absolute Variance Swap, receives a payment of $5,000 from Beta. This example illustrates how the swap allows Alpha to profit from higher-than-expected absolute price dispersion without directly owning the index or being exposed to its directional movements, while potentially having a smoother payoff profile than a standard variance swap due to the "absolute" consideration. The settlement is typically in cash.

Practical Applications

While "Absolute Variance Swaps" are not as widely traded as their conventional counterparts, their conceptual applications mirror and extend those of traditional variance and volatility swaps, particularly for sophisticated market participants. These applications include:

• Hedging Volatility Exposure: Institutional investors and portfolio managers could use Absolute Variance Swaps to protect their portfolios against unexpected changes in price dispersion. For instance, a manager concerned about potential increases in absolute price movements could buy an Absolute Variance Swap to offset losses in their equity holdings, especially those sensitive to extreme market events.¹⁶,¹⁵,¹⁴
• Speculation on Dispersion: Traders with a specific view on future absolute price movements of an underlying asset, independent of its direction, could use these swaps to express that view. If they anticipate greater absolute price swings than implied by the market, they could take a long position.¹³,¹²
• Portfolio Diversification: Adding derivatives like Absolute Variance Swaps can aid in portfolio diversification by providing exposure to a distinct risk factor (volatility/dispersion) that often behaves differently from traditional asset classes.¹¹
• Structured Products: Financial institutions may incorporate such swaps into tailored structured notes or other derivative products to offer clients customized solutions for volatility exposure, without direct involvement in the underlying asset.¹⁰
• Risk Recycling: Dealers with substantial structured products businesses often find themselves short correlation and can use instruments like variance or potentially absolute variance swaps to manage these exposures, engaging in strategies like dispersion trades.⁹

The Commodity Futures Trading Commission (CFTC) oversees derivatives markets in the U.S., including swaps, to ensure market integrity and transparency. The CFTC sets swap data reporting and recordkeeping requirements for various financial instruments, including volatility and variance swaps, to enable regulatory oversight and systemic risk mitigation.⁸,⁷

Limitations and Criticisms

The primary limitation of an "Absolute Variance Swap," as a distinct product, is its lack of widespread standardization and liquidity compared to traditional variance or volatility swaps. This can lead to higher bid-ask spreads and difficulty in finding counterparties. Furthermore, like all over-the-counter (OTC)) derivatives, pricing and valuation can be more complex, often relying on bespoke models and assumptions.

Beyond these market-specific issues, any derivative exposed to volatility carries inherent risks:

• Basis Risk: There can be a mismatch between the theoretical realized variance calculated by the swap and the actual volatility experienced by a hedged portfolio, leading to imperfect hedging outcomes.
• Model Dependence: The valuation and replication of such complex derivatives often depend on sophisticated financial models, which, if based on incorrect assumptions, can lead to mispricing or unexpected losses. Issues can arise in replicating payoffs, particularly with discrete sampling of returns.⁶
• Tail Risk: While an "absolute" component might reduce some of the extreme convexity, market movements that drastically exceed expectations, commonly referred to as "tail events," can still lead to significant and rapid changes in the swap's value, potentially resulting in substantial losses for the selling party. The challenge of accurately forecasting future volatility remains a core limitation for both parties to the swap.⁵

Academic research into volatility derivatives consistently highlights the complexities of their pricing and the potential for large losses if hedging strategies are not perfectly executed, especially in volatile market conditions.⁴

Absolute Variance Swap vs. Variance Swap

The distinction between an Absolute Variance Swap and a variance swap lies primarily in how the "variance" component, or measure of dispersion, is treated and calculated, particularly concerning the use of absolute values.

While a standard variance swap measures the average of squared deviations from the mean (realized variance), an "Absolute Variance Swap" would theoretically involve some form of absolute value in its calculation or payoff. This could mean it's designed to provide exposure to a measure like the mean absolute deviation squared, or perhaps refers to a swap on absolute volatility where the payoff is then squared to align with "variance" terminology. The more common, related product explicitly mentioned in market literature is the "absolute volatility swap," which pays out based on absolute realized volatility.²

FAQs

1. How is an Absolute Variance Swap different from a Volatility Swap?

An Absolute Variance Swap, conceptually, focuses on a measure of price dispersion that incorporates absolute differences, and the term "variance" implies squaring. A Volatility Swap, on the other hand, directly exchanges realized volatility (the standard deviation) against a fixed volatility strike, without squaring the final payoff measure.¹ This means a volatility swap's payoff is linear in volatility, while a variance swap (and conceptually, an Absolute Variance Swap if it retains some squared component) has a different relationship to volatility.

2. Why would an investor use an Absolute Variance Swap instead of just buying options?

Unlike option contracts, which are influenced by multiple factors like the underlying asset's price direction (delta), time decay (theta), and volatility (vega), an Absolute Variance Swap aims to provide a "pure play" on the magnitude of price movements. This means investors gain exposure to dispersion without taking a directional view on the underlying asset, simplifying their speculation or hedging strategy on volatility.

3. Are Absolute Variance Swaps widely traded?

No, the term "Absolute Variance Swap" is not as widely recognized or traded as standardized variance swaps or volatility swaps. While the concept of derivatives incorporating "absolute" measures exists (such as the "absolute volatility swap"), a distinct "Absolute Variance Swap" is less common in mainstream financial markets. Most volatility trading occurs through variance swaps, volatility swaps, or traditional options.