Absolute volatility swap: Meaning, Criticisms & Real-World Uses

What Is Absolute Volatility Swap?

An absolute volatility swap is a derivative contract where two parties agree to exchange payments based on the realized absolute volatility of an underlying asset over a specified period, against a predetermined fixed volatility rate (the strike volatility). This financial instrument falls under the broader category of derivatives, specifically within the realm of volatility derivatives. Unlike a standard variance swap, which deals with squared volatility, an absolute volatility swap directly targets the standard deviation of returns, providing a more intuitive measure of price dispersion. Participants use absolute volatility swaps to speculate on, or hedge against, changes in the magnitude of price movements in an asset, independent of the direction of those movements.

History and Origin

The concept of trading volatility as an asset class began to gain traction in the financial markets in the late 20th century. While early derivatives focused on directional price movements, the demand for instruments that isolated volatility as a tradable component grew. The Chicago Board Options Exchange (CBOE) launched the original VIX Index in 1993, initially measuring the implied volatility of S&P 100 Index options.¹³,¹² This marked a significant step toward making volatility a more transparent and accessible measure. Later, in 2003, the CBOE, in collaboration with Goldman Sachs, updated the VIX methodology to base it on the S&P 500 Index, further solidifying its role as a key market barometer for expected volatility.¹¹,¹⁰,⁹

This evolution of volatility indices and the underlying theoretical frameworks for pricing options led to the development of over-the-counter (OTC) volatility derivatives, including absolute volatility swaps. These instruments emerged from the need for more precise and tailored ways to manage or take exposure to volatility, building on the foundational understanding provided by variance swaps.

Key Takeaways

An absolute volatility swap is an OTC derivative contract that allows parties to exchange payments based on realized absolute volatility versus a fixed strike volatility.
It provides direct exposure to the standard deviation of returns, differing from variance swaps that focus on squared volatility.
These swaps are used for both speculation on future volatility levels and for hedging existing portfolio risk.
The payoff of an absolute volatility swap is linear to the difference between realized volatility and the strike volatility.
Pricing and replication can be more complex than for variance swaps due to the non-linear nature of standard deviation.

Formula and Calculation

The payoff of an absolute volatility swap at maturity is determined by the difference between the realized absolute volatility of the underlying asset and the agreed-upon strike volatility, multiplied by a notional amount.

The realized absolute volatility, often denoted as (\sigma_{realized}), is typically calculated as the annualized standard deviation of the asset's daily logarithmic returns over the life of the swap.

The payoff for the party receiving realized volatility (the "long volatility" party) and paying the strike volatility is:

\text{Payoff} = \text{Notional} \times (\sigma_{realized} - K_{\text{vol}})

Where:

(\text{Notional}) = The agreed-upon monetary amount per percentage point of volatility.
(\sigma_{realized}) = The annualized realized standard deviation of the underlying asset's logarithmic returns over the swap's term.
(K_{\text{vol}}) = The fixed volatility strike rate, agreed upon at the inception of the swap.

The calculation of realized volatility involves computing the standard deviation of daily logarithmic returns and then annualizing it by multiplying by the square root of the number of trading days in a year (e.g., (\sqrt{252}) for equities). This contrasts with variance swaps, where the realized variance (squared standard deviation) is the basis of the payoff.

Interpreting the Absolute Volatility Swap

Interpreting an absolute volatility swap involves understanding the market's expectation of future price movements. If a trader believes that the actual (realized) volatility of an asset will be higher than the strike volatility of the swap, they would go long the absolute volatility swap. Conversely, if they anticipate lower realized volatility, they would go short.

The strike volatility for an absolute volatility swap is determined by market supply and demand and reflects the consensus expectation of the underlying asset's future volatility. A higher strike indicates an expectation of greater price fluctuations, while a lower strike suggests anticipated stability. The difference between the realized volatility and the strike at maturity directly translates into the profit or loss. For instance, if the realized volatility is 20% and the strike is 18% with a notional of $1 million per percentage point, the long party receives $20,000. This direct relationship to standard deviation makes it a more intuitive measure of market volatility compared to variance.

Hypothetical Example

Consider an absolute volatility swap on XYZ stock with a notional amount of $100,000 per volatility point and a strike volatility of 25%. The swap has a term of three months.

Over the three-month period, suppose XYZ stock experiences daily logarithmic returns. To calculate the realized absolute volatility, we would first compute the standard deviation of these daily returns.

Let's assume the daily logarithmic returns for XYZ over the three months are:
Day 1: 0.005, Day 2: -0.010, Day 3: 0.008, ..., Day N: 0.012

After calculating the standard deviation of these daily returns, we annualize it. For example, if the calculated daily standard deviation is 0.015, the annualized realized volatility would be:

\sigma_{realized} = 0.015 \times \sqrt{252} \approx 0.2381 \text{ or } 23.81\%

At maturity, the realized absolute volatility is 23.81%. Since the strike volatility was 25%, the payoff for the party that is long volatility would be:

\text{Payoff} = \$100,000 \times (0.2381 - 0.25) = \$100,000 \times (-0.0119) = -\$1,190

In this scenario, the party long the absolute volatility swap would pay $1,190 to the counterparty, as the realized volatility was lower than the strike. This example illustrates how the payoff directly reflects the difference in volatility points.

Practical Applications

Absolute volatility swaps serve several practical purposes in financial markets, primarily within the realm of risk management and speculative trading.

Hedging Volatility Exposure: Investment managers with portfolios sensitive to market fluctuations can use absolute volatility swaps to hedge against unexpected changes in volatility. For example, a portfolio of long options, which benefits from increasing volatility, could be hedged by shorting an absolute volatility swap if the manager anticipates a decline in future price movements. Conversely, if a portfolio is negatively impacted by rising volatility, a long position in an absolute volatility swap can provide a hedge.⁸
Speculation: Traders who have a directional view on future volatility but not on the underlying asset's price can use absolute volatility swaps to express that view. If they believe volatility will increase, they can buy the swap; if they believe it will decrease, they can sell it. This allows for a pure play on volatility, separate from the asset price itself.
Arbitrage Opportunities: Sophisticated investors may identify discrepancies between implied volatility (derived from options prices) and their forecast of realized volatility. An absolute volatility swap can be used as part of an arbitrage strategy to profit from these perceived mispricings.
Portfolio Diversification: Adding volatility as an asset class through instruments like absolute volatility swaps can contribute to portfolio diversification, as volatility often behaves independently of or inversely to asset prices, especially during periods of market stress. The International Monetary Fund (IMF) regularly discusses global financial stability and market volatility in its Global Financial Stability Report.⁷,⁶,⁵

Limitations and Criticisms

While absolute volatility swaps offer targeted exposure to volatility, they come with certain limitations and criticisms.

OTC Market and Counterparty Risk: Absolute volatility swaps are typically traded in the over-the-counter (OTC) market, meaning they are customized agreements between two parties rather than traded on an exchange. This exposes participants to counterparty risk—the risk that the other party to the contract will default on its obligations. This risk is generally higher than with exchange-traded derivatives, which are often centrally cleared.
Pricing Complexity: Accurately pricing an absolute volatility swap can be complex. Unlike variance, which can be replicated with a static portfolio of options, replicating absolute volatility is theoretically more challenging and may require dynamic hedging strategies. This complexity can lead to wider bid-ask spreads and less transparency in pricing compared to simpler derivatives.
Liquidity: Due to their customized nature and OTC trading, absolute volatility swaps may suffer from lower liquidity compared to standardized exchange-traded options or futures. This illiquidity can make it difficult to unwind a position before maturity without incurring significant costs.
Regulatory Scrutiny: The use of derivatives by financial institutions, including swaps, has been subject to increased regulatory scrutiny, particularly since the 2008 financial crisis. For example, the U.S. Securities and Exchange Commission (SEC) adopted Rule 18f-4 in 2020 to modernize the regulatory framework for derivatives use by registered funds, aiming to enhance investor protections.,,⁴ ³T²his regulatory environment can impact how financial institutions use and account for these instruments.
Model Risk: The valuation and risk management of absolute volatility swaps rely heavily on mathematical models. If these models are flawed or based on incorrect assumptions, it can lead to significant losses.

Absolute Volatility Swap vs. Variance Swap

Absolute volatility swaps and variance swaps are both volatility derivatives, but they differ fundamentally in how they measure and pay out based on volatility. This distinction is crucial for understanding their respective uses and risk profiles.

Feature	Absolute Volatility Swap	Variance Swap
Volatility Measure	Realized absolute volatility (standard deviation of returns)	Realized variance (squared standard deviation of returns)
Payoff Function	Linear to the difference between realized volatility and strike volatility	Linear to the difference between realized variance and strike variance
Replication	More complex; often requires dynamic hedging	Simpler; can be replicated with a static portfolio of options
Sensitivity	Directly reflects percentage point changes in volatility	Reflects squared percentage changes in volatility
Intuition	More intuitive, as it's the widely understood measure of risk	Less intuitive, as variance is squared volatility
Market Standard	Less common in standard market indices	Forms the basis for the calculation of many volatility indices, like the VIX

The key difference lies in the payoff structure. An absolute volatility swap pays based on the standard deviation, offering a direct and proportional exposure to the volatility level. In contrast, a variance swap pays based on the square of the standard deviation. This squared relationship means that a variance swap's payoff accelerates as volatility increases, leading to a convex payout profile. This makes variance swaps more sensitive to large changes in volatility compared to absolute volatility swaps, which have a more linear payoff. The relative simplicity of replicating a variance swap using a portfolio of options has historically made it a more common instrument in the derivatives market.

FAQs

What is the primary difference between an absolute volatility swap and a variance swap?

The primary difference lies in their payoff structure: an absolute volatility swap's payoff is based on the realized standard deviation of returns, while a variance swap's payoff is based on the realized variance (the square of the standard deviation). This means the absolute volatility swap has a linear payoff with respect to volatility, whereas the variance swap has a quadratic payoff.

How is the strike volatility determined in an absolute volatility swap?

The strike volatility for an absolute volatility swap is negotiated between the two counterparties in the OTC market. It reflects the market's collective expectation of the underlying asset's future realized absolute volatility over the life of the swap.

Can an absolute volatility swap be used for hedging?

Yes, absolute volatility swaps are commonly used for hedging. Investors with portfolios sensitive to changes in market volatility can use these swaps to offset potential losses or gains stemming from unexpected increases or decreases in volatility, providing a form of portfolio hedging.

Are absolute volatility swaps exchange-traded?

Typically, absolute volatility swaps are traded in the over-the-counter (OTC) market, meaning they are customized contracts negotiated directly between two parties. They are not standardized products traded on public exchanges like stocks or futures.