Volatility Swap

A volatility swap provides direct exposure to the volatility of an underlying asset's returns, isolated from directional price moves. The payoff is based on the difference between the realized volatility over the contract period and a pre-agreed strike volatility. This makes it a cleaner hedge or speculative instrument for volatility itself, unlike options where price (delta) and time decay (theta) are factors.

• Key Mechanism: Settlement = Notional Amount × (Realized Vol - Strike Vol)
• Example: A trader buys a 1-month BTC volatility swap with a 60% strike. If realized volatility is 80%, they profit on the 20% difference.

The core of the swap's payoff hinges on the calculation of realized volatility, which is the actual historical volatility observed during the contract's life, typically measured as the standard deviation of daily log returns. This is contrasted with the fixed implied volatility (the strike), which is the market's forward-looking expectation priced into the contract at inception.

• Calculation: Realized volatility is computed from high-frequency or daily price data.
• Importance: The trader is betting that their forecast of future realized volatility differs from the market's implied forecast.

Volatility swaps are cash-settled derivatives; no physical delivery of the underlying asset occurs. The contract size is defined by a vega notional amount, which determines the cash value of a one-point (e.g., 1%) move in volatility.

• Payoff Formula: Cash Flow = Vega Notional × (σ_realized - σ_strike)
• Example: A vega notional of $100,000 means each 1% difference in volatility results in a $100,000 gain or loss. A positive result is paid by the seller to the buyer.

While both are volatility derivatives, key differences exist. A variance swap pays off based on the difference between realized and strike variance (volatility squared). This leads to a convexity effect, making variance swaps more sensitive to large price moves (volatility of volatility). Volatility swaps are linear in volatility, providing simpler, direct exposure.

• Sensitivity: Variance swaps have positive vega convexity; volatility swaps do not.
• Hedging: Volatility swaps are often used to hedge vega exposure more precisely.

These instruments are used for speculation, hedging, and volatility arbitrage. Traders use them to express a view on future volatility without a directional bias on the asset's price.

• Speculation: Betting that future realized volatility will be higher or lower than the implied volatility priced in.
• Hedging: Portfolio managers hedge against changes in market volatility (vega risk).
• Arbitrage: Exploiting pricing discrepancies between volatility swaps, variance swaps, and options markets.

While traded OTC traditionally, DeFi protocols enable on-chain volatility swaps using options vaults and oracles. The payoff can be replicated dynamically using a portfolio of options (options strip) through model-driven delta-hedging, though this introduces complexity and tracking error.

• Replication Challenge: Requires continuous rebalancing of an options portfolio to maintain pure volatility exposure.
• On-Chain: Smart contracts use oracles to calculate realized volatility and automate cash settlement.

A volatility swap is a forward contract on the realized volatility of an asset. The payoff is based on the difference between the realized volatility and a pre-agreed strike volatility. Key components include:

• Underlying Asset: Typically a crypto index (e.g., BTC, ETH) or a DeFi token.
• Vega Notional: The contract's sensitivity to a 1% change in volatility.
• Settlement: Cash-settled based on the annualized standard deviation of the asset's returns over the contract period.

Pricing is complex and relies on models beyond Black-Scholes. Key inputs are derived from the volatility surface of options markets.

• Implied Volatility (IV): The market's forecast of future volatility, extracted from option prices.
• Variance Swaps: A closely related instrument where the payoff is based on realized variance (volatility squared). Volatility swaps are often priced and hedged using variance swaps.
• Volatility Risk Premium: The typical difference where implied volatility exceeds realized volatility, a key source of return for sellers.

These instruments are primarily used for pure volatility exposure.

• Portfolio Hedging: Institutions hedge against increases in market volatility (a "volatility spike") that can negatively impact portfolios.
• Dispersion Trading: Exploiting differences in volatility between an index and its components.
• Delta-Neutral Strategies: Allows traders to profit from volatility changes without taking a directional bet on the asset's price.

Volatility swaps are well-established in TradFi, providing a blueprint for crypto.

• VIX Futures & Options: Trade on the CBOE Volatility Index, the market's "fear gauge" for the S&P 500.
• Over-the-Counter (OTC) Markets: Large institutional deals are brokered by investment banks.
• Key Difference: DeFi versions like Squeeth are perpetual and non-expiring, unlike fixed-term TradFi contracts.

Trading volatility derivatives carries unique risks:

• Model Risk: Incorrect pricing models can lead to significant losses.
• Hedging Error (Gamma Risk): Dynamic delta-hedging is imperfect, especially during large price moves ("gap risk").
• Liquidity Risk: The DeFi market for these instruments is nascent and can be illiquid.
• Funding Rate Risk: In perpetual structures, funding payments can erode returns.

A volatility swap's value is directly tied to vega, its sensitivity to changes in implied volatility. This exposure is complicated by the volatility smile—the observed pattern where implied volatility differs for options at various strike prices. Mispricing the smile or shifts in its shape can lead to significant mark-to-market losses, even if the realized volatility is correctly forecast.

The contract's payoff depends on the precisely defined formula for calculating realized volatility. Key variables include:

• Sampling frequency: Daily vs. intraday sampling can yield different results.
• Observation days: The number of trading days in the calculation period.
• Mean return assumption: Whether the calculation uses the standard deviation of returns or assumes a zero mean. Disputes can arise if the calculation methodology is not contractually explicit.

As an over-the-counter (OTC) derivative, a volatility swap carries counterparty credit risk. The party owing the payout at settlement may default. This risk is often mitigated by posting collateral in a margin account, which introduces liquidity risk from margin calls. On-chain versions using smart contracts replace this with smart contract risk and oracle risk, where the volatility feed must be secure and manipulation-resistant.

The market for volatility swaps, especially for bespoke tenors or underlyings, can be illiquid, making it difficult to exit or adjust a position without incurring large bid-ask spreads. Gap risk (or jump risk) is a major concern: a sudden, large price move in the underlying asset can cause a discontinuous leap in realized volatility, leading to a payout that static delta-hedging strategies cannot adequately cover.

Dealers typically hedge a short volatility swap position by dynamically trading a portfolio of vanilla options to replicate the volatility exposure. This process is complex and costly due to:

• Transaction costs from frequent rebalancing.
• Gamma/theta trade-off: Hedging volatility requires managing the decay (theta) and convexity (gamma) of the option portfolio.
• Model risk: The hedge's effectiveness depends on the accuracy of the options pricing model used.

When used as a hedge, a basis risk emerges if the volatility swap's payoff does not perfectly correlate with the volatility exposure being hedged. For example, hedging the volatility of a specific portfolio with a swap on a broad market index (like the VIX) is imperfect. The hedge may fail if the portfolio's volatility diverges from the index's volatility, leaving residual risk.

A closely related derivative where the payoff is based on the realized variance (volatility squared) of the underlying asset. Unlike a volatility swap, its payoff is convex with respect to volatility, meaning its value is more sensitive to large volatility spikes. Settlement uses the formula: Notional * (Realized Variance - Variance Strike). This convexity leads to a variance risk premium, as sellers typically demand compensation for the tail risk.

The CBOE Volatility Index, known as the "fear gauge," measures the market's expectation of 30-day volatility implied by S&P 500 index options. It is the foundational benchmark for volatility trading. Volatility swaps and variance swaps are often priced and settled against the realized value of the VIX or similar indices, making it a critical reference point for these derivatives.

Volatility swaps are a direct alternative to complex options strategies like straddles for expressing a view on future volatility. Key distinctions:

• Options: Payoff depends on both direction and volatility; involves delta hedging.
• Volatility Swap: Pure volatility exposure; no delta risk. The swap's fixed strike is directly comparable to the implied volatility priced into options markets, allowing traders to arbitrage differences between implied and realized volatility.

The core mechanism defining the floating leg of the swap. It is typically calculated as the annualized standard deviation of the underlying asset's logarithmic returns over the contract period. The formula is: σ_realized = sqrt(252/N * Σ (ln(P_t/P_{t-1}))^2). Critical contract specifications include:

• Observation Frequency: Daily closing prices are standard.
• Day Count Convention: Usually 252 business days per year.
• Mean Return: Often assumed to be zero for simplicity.

A simpler OTC contract that locks in a future volatility level for a specific period. It is a forward-starting bet on volatility, often structured as a cash-settled difference payment. While similar to a swap, an FVA is typically a single payment instrument for a forward period, whereas a volatility swap can have a running lifetime. It acts as a building block for structuring more complex volatility derivatives.

Exchange-Traded Products (like VXX) that provide exposure to short-term volatility futures, often tracking the VIX. These are the most accessible public instruments for volatility exposure. Unlike a direct volatility swap, these products suffer from roll cost and contango decay in futures markets, which can cause significant tracking error versus spot volatility. They represent a packaged, tradable form of volatility risk.