Active variance swap

Active Variance Swap

An Active Variance Swap is a type of derivative contract that allows financial market participants to speculate on or hedge against the future statistical variance of an underlying asset's price, or to trade its volatility. Unlike a traditional variance swap which typically covers a predetermined, fixed period, an "active" variance swap may imply a more dynamic trading or management approach, often involving ongoing adjustments or positions taken based on changing market conditions. As a sophisticated instrument within financial derivatives, it offers direct exposure to the squared future realized volatility of an asset, independent of its directional price movement.

History and Origin

The concept of volatility trading gained significant traction in the financial markets during the late 1990s, with variance swaps emerging as a key instrument. Academic and industry papers, such as those by Demeterfi, Derman, Kamal, and Zou in 1999, formalized the pricing and hedging of these instruments, paving the way for their broader adoption⁸. These early works demonstrated how variance could be replicated using a portfolio of options contracts across a continuum of strike prices.

While volatility-based products existed prior, variance swaps offered a cleaner, more direct way to trade volatility compared to traditional options contracts. Their introduction allowed investors to isolate a bet on future price fluctuations. However, the market for volatility derivatives faced significant challenges during periods of extreme market turbulence, such as the 2008 financial crisis, when unforeseen volatility levels made hedging more difficult and liquidity scarce⁷. Despite these challenges, the underlying theory and utility of variance swaps have ensured their continued, albeit specialized, presence in the derivatives landscape.

Key Takeaways

• An Active Variance Swap allows investors to gain direct exposure to the future realized volatility of an underlying asset.
• The payoff of a variance swap is tied to the squared difference between the asset's return and its mean, providing a clean volatility bet.
• These instruments are primarily traded Over-the-Counter (OTC) between institutional investors, banks, and hedge funds.
• Active Variance Swaps can be used for both speculation on future market turbulence or for hedging existing portfolio exposures to volatility.
• Their value is sensitive to the shape of the implied volatility curve and the frequency of observations used in calculating realized variance.

Formula and Calculation

The payoff of a variance swap at expiration is typically calculated as:

Where:

• ( N ) is the Notional Value or "vega notional," which converts the variance difference into a monetary amount. Often expressed as dollar per annualized volatility point squared.
• (\text{Realized Variance} ) is the actual variance of the underlying asset's logarithmic returns over the life of the swap. It is usually calculated as: $$\text{Realized Variance} = \frac{A}{A-1} \sum_{i=1}^{A} \left( \ln\left(\frac{S_i}{S_{i-1}}\right) \right)^2 \times \frac{252}{\text{Observation Days}}$$ Here, ( S_i ) is the asset price at observation (i), ( A ) is the total number of observations, and 252 is often used as the number of trading days in a year to annualize the variance. The term (\frac{A}{A-1}) is a bias correction for small samples.
• (\text{Variance Strike} ) is the predetermined variance level agreed upon at the initiation of the Active Variance Swap. This strike is typically set to make the initial value of the swap zero.

The realized variance is based on historical price movements. The logarithmic returns are used because they are approximately additive, making the variance calculation more straightforward and consistent.

Interpreting the Active Variance Swap

Interpreting an Active Variance Swap involves understanding that one party is paying a fixed variance strike, while the other pays the realized volatility of the underlying asset squared. If the realized variance of the asset's returns over the swap's observation period is higher than the agreed-upon variance strike, the buyer of the swap (receiver of realized variance) profits. Conversely, if the realized variance is lower than the strike, the seller of the swap (payer of realized variance) profits.

This allows for a direct pure play on the expected variability of an asset, independent of whether its price goes up or down. Investors interpret the variance strike as the market's expectation for future variance. Therefore, entering an Active Variance Swap means taking a view on whether future volatility will be higher or lower than currently priced into the derivative. This makes it a valuable tool for risk management and directional volatility trading.

Hypothetical Example

Consider an investor, ABC Fund, who believes that the upcoming earnings announcement and product launch for TechCorp will lead to significantly higher volatility in TechCorp's stock price over the next three months, regardless of whether the stock goes up or down. They decide to enter an Active Variance Swap with XYZ Bank.

• Underlying Asset: TechCorp Stock
• Term: 3 months (63 trading days)
• Notional Value (N): $100,000 per annualized variance point squared
• Variance Strike: 0.04 (corresponding to a volatility of (\sqrt{0.04} = 0.20) or 20% annualized)

Over the next three months, TechCorp's stock experiences significant price swings due to the news. At expiration, the realized volatility of TechCorp's stock, calculated based on its daily logarithmic returns over the 63 trading days, is determined to be 0.06 (or 24.5% annualized volatility).

The payoff for ABC Fund (the buyer of the Active Variance Swap) is calculated as:

In this scenario, ABC Fund receives $2,000 from XYZ Bank because the actual realized volatility of TechCorp's stock exceeded the strike price agreed upon in the Active Variance Swap. This example illustrates how the Active Variance Swap allows for direct speculation on future price variability, providing a gain even if the underlying asset's price ends up lower, as long as its path included significant fluctuations.

Practical Applications

Active Variance Swaps are utilized by sophisticated investors for several strategic purposes:

• Speculation on Volatility: Investors who anticipate significant changes in market volatility but are uncertain about the direction of asset prices can use Active Variance Swaps. For instance, before major economic announcements or political events, a fund might buy an Active Variance Swap if it expects increased market turbulence.
• Hedging Volatility Exposure: Funds with large portfolios of options contracts or other volatility-sensitive instruments can use Active Variance Swaps to offset their exposure to changes in future realized volatility. This provides a cleaner hedge than simply trading futures contracts on volatility indexes.
• Arbitrage Strategies: Experienced traders may identify discrepancies between the implied volatility priced into options contracts and the expected realized volatility that can be captured via Active Variance Swaps. They can then execute strategies to profit from these mispricings.
• Portfolio Risk Management: For institutional portfolios sensitive to large price swings, Active Variance Swaps can serve as an effective tool to manage the impact of unexpected market movements without taking a directional stance on the underlying asset.

The Over-the-Counter (OTC) nature of these derivatives means they are customizable, allowing market participants to tailor the notional value and strike to their specific needs. The over-the-counter derivatives market, while experiencing seasonal fluctuations, saw its notional outstanding value reach $667 trillion by the end of 2023⁶. Regulatory efforts, such as the Dodd-Frank Act in the United States, have aimed to increase transparency and reduce systemic risk in these markets by requiring standardized swaps to be traded on regulated facilities and mandating reporting to swap data repositories⁴, ⁵.

Limitations and Criticisms

While Active Variance Swaps offer unique benefits, they also come with inherent limitations and criticisms:

• Liquidity Risk: As Over-the-Counter (OTC) instruments, Active Variance Swaps are not as liquid as exchange-traded products. This can make it challenging to exit positions before maturity without impacting the price, especially in stressed market conditions. The volatility derivatives market experienced significant turmoil and reduced liquidity during the 2008-2009 credit crisis², ³.
• Counterparty Risk: Since these are bilateral contracts, both parties are exposed to the risk that the other party may default on its obligations. While increased use of Central Counterparty Clearing (CCP) for many standardized derivative contracts has mitigated this to some extent, many customized variance swaps may still be subject to bilateral clearing arrangements.
• Complex Pricing and Hedging: The theoretical pricing and hedging of variance swaps relies on continuous observation of the underlying asset's price and dynamic trading of a portfolio of options contracts across all strike prices¹. In practice, discrete observations and the limited availability of options across the full strike spectrum introduce hedging errors. Jumps in asset prices, which are not perfectly captured by continuous models, can also complicate hedging strategies.
• Sensitivity to Skew and Kurtosis: While designed to be a pure play on variance, their practical pricing and hedging can be sensitive to higher-order moments of the return distribution, such as skewness (asymmetry) and kurtosis (fat tails), which are reflected in the implied volatility smile or skew. This can introduce biases in the strike price.

Active Variance Swap vs. Volatility Swap

Active Variance Swaps and Volatility Swaps are both derivative instruments used to trade future volatility. The key difference lies in their payoff structure and the linearity of their exposure to volatility.

A Volatility Swap has a payoff that is linearly proportional to the difference between the realized volatility (standard deviation) and a pre-agreed volatility strike. This means that for every percentage point the realized volatility exceeds the strike, the holder of the swap earns a fixed amount, and vice-versa.

An Active Variance Swap, on the other hand, has a payoff that is linear in variance (the square of volatility). This means its payoff is convex with respect to volatility. If the realized volatility is high, the squared term amplifies the difference, leading to potentially larger gains or losses compared to a linear volatility swap for the same change in volatility. This convexity property makes variance swaps generally easier to replicate and hedge using a static portfolio of options contracts because the theoretical replication strategy for variance is simpler than for volatility. The "active" aspect of the variance swap refers to the dynamic approach to managing or taking positions in these instruments.

Confusion often arises because both instruments are designed to trade volatility. However, the fundamental difference in their linear or squared relationship to volatility means they have different risk management profiles and hedging characteristics.

FAQs

What is the primary purpose of an Active Variance Swap?

The primary purpose of an Active Variance Swap is to allow investors to take a direct position on the future level of an asset's price volatility, specifically its variance, without being exposed to the asset's directional price movements. It enables speculation or hedging based purely on how much an asset's price is expected to fluctuate.

How is the "realized variance" calculated for a swap?

Realized variance for a variance swap is typically calculated by summing the squared daily logarithmic returns of the underlying asset over the observation period, and then annualizing the result. The specific calculation method, including the number of observations and the annualization factor, is defined in the swap agreement.

Who typically uses Active Variance Swaps?

Active Variance Swaps are complex derivative instruments primarily used by institutional market participants, such as hedge funds, investment banks, and proprietary trading desks. These entities use them for sophisticated hedging, speculation, and arbitrage strategies involving market volatility.

Are Active Variance Swaps exchange-traded?

Most Active Variance Swaps are traded Over-the-Counter (OTC), meaning they are customized bilateral agreements between two parties rather than standardized contracts traded on an exchange. While some volatility-related products are exchange-traded (e.g., VIX futures contracts), variance swaps often offer greater flexibility in terms of underlying asset, tenor, and notional value.