Variance Swap: Definition, How It Works, and Comparison with Volatility Swap

August 24, 2024 4 min read Finance Investments Variance Swap Volatility Swap Financial Derivatives Hedging Speculation

A detailed exploration of variance swaps, including their definition, operational mechanics, and a comparison with volatility swaps.

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Variance swaps are financial derivatives designed to allow investors to hedge or speculate on the volatility of an underlying asset. Unlike traditional options, these swaps provide direct exposure to the variance (the square of volatility) of returns, rather than the price movements themselves.

Definition

A variance swap is a forward contract on the realized variance of an asset’s returns. The payoff for the variance swap is determined by the difference between the realized variance during the period and the strike variance agreed upon at the inception of the contract.

In mathematical terms, the payoff of a variance swap can be represented as:

\text{Payoff} = (\overline{\sigma^2} - K_\text{var}) \times \text{Notional Amount}

where:

$\overline{\sigma^2}$ is the realized variance,
$K_\text{var}$ is the strike variance.

How Variance Swaps Work

Mechanics

Contract Initiation: Two parties agree on a notional amount, the strike variance, and the maturity of the swap.
Observation Period: Over the life of the swap, the price of the underlying asset is monitored at specified intervals.
Calculation of Realized Variance: The realized variance is calculated based on the observed price fluctuations.
Settlement: At maturity, the payoff is calculated based on the difference between the realized variance and the strike variance, adjusted by the notional amount.

Practical Uses

Variance swaps are utilized for various purposes, including:

Hedging: Investors can hedge against volatility risk in their portfolios. For example, an equity fund manager may use a variance swap to mitigate the impact of sudden market volatility.
Speculation: Traders can speculate on future volatility without taking a directional bet on the underlying asset’s price.

Comparison with Volatility Swaps

Volatility Swaps

Volatility swaps are similar to variance swaps but offer a direct exposure to the actual volatility rather than its square. The payoff of a volatility swap is linear with respect to volatility:

\text{Payoff} = (\overline{\sigma} - K_\text{vol}) \times \text{Notional Amount}

where:

$\overline{\sigma}$ is the realized volatility (not the variance),
$K_\text{vol}$ is the strike volatility.

Key Differences

Exposure: Variance swaps give exposure to the variance of returns, while volatility swaps give exposure to the volatility.
Payoff Profile: The payoff in variance swaps is quadratic (variance) versus linear (volatility) in volatility swaps.
Applications: Variance swaps may be more suitable for precise hedging strategies, whereas volatility swaps might be preferred for straightforward speculation on volatility levels.

Special Considerations

Understanding the nuances of variance swaps is crucial:

Smile Risk: Variance swaps are affected by volatility skew or smile, which reflects the market’s varying volatility expectations for different strike prices.
Liquidity and Pricing: While variance swaps can be tailored, they may suffer from liquidity issues as opposed to standardized options.
Counterparty Risk: The parties involved must consider the financial stability of the counterparty to mitigate default risk.

Example

Consider an investor who enters into a variance swap with a strike variance of 0.04 (or 4%) and a notional amount of $1,000,000. At maturity, if the realized variance is 0.06 (or 6%), the payoff would be:

(\overline{\sigma^2} - K_\text{var}) \times \text{Notional Amount} = (0.06 - 0.04) \times $1,000,000 = $20,000

Historical Context

The concept of variance swaps emerged in the 1990s, catering to the growing need for volatility trading tools among institutional investors. These instruments have since evolved, offering more sophisticated ways to manage and capitalize on volatility.

Implied Volatility: The market’s forecast of a likely movement in an asset’s price.
Delta Hedging: A strategy to reduce the direction risk of a position in options.
Gamma: The rate of change of delta with respect to the underlying asset’s price.

FAQs

Q: Can retail investors use variance swaps?
A: Generally, variance swaps are complex instruments and are more suitable for institutional investors due to their sophisticated risk profiles.

Q: What happens if the realized variance is lower than the strike variance?
A: If the realized variance is lower, the seller of the variance swap pays the difference, leading to a negative payoff for the holder.

Q: How is realized variance calculated?
A: Realized variance is typically calculated using the squared returns of the underlying asset over the observation period.

References

Hull, J.C. (2022). Options, Futures, and Other Derivatives. Pearson.
Black, F., Scholes, M. (1973). “The Pricing of Options and Corporate Liabilities”. Journal of Political Economy, 81(3), 637-654.
Carr, P., & Madan, D. (1998). “Towards a Theory of Volatility Trading”. Volatility: New Estimation Techniques for Pricing Derivatives.

Summary

Variance swaps offer a sophisticated mechanism for hedging and speculating on the variance of asset returns. By understanding their mechanics, applications, and differences from related instruments like volatility swaps, investors can effectively utilize these derivatives to manage volatility risk.