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VIX

The CBOE Volatility Index (VIX) is a real-time market index that measures the expected of the Index over the next 30 days, derived from the prices of a wide range of out-of-the-money options. Often referred to as the "fear gauge," it serves as a key indicator of sentiment regarding near-term , with higher values signaling greater anticipated fluctuations in prices. Introduced by the (CBOE) in 1993 as the original volatility index based on Index (OEX) options, the VIX was redesigned in 2003 to use Index (SPX) options for broader market representation and improved accuracy in estimating forward-looking volatility. This model-free methodology calculates the VIX using the prices of near-term and next-term SPX options (typically 23 to 37 days to expiration) spanning a wide range of strike prices, interpolating to a constant 30-day horizon, and expressing the result as an annualized percentage. The formula involves the square root of the rate, weighted by option strike prices, ensuring it reflects the market's consensus on potential movements without assuming a specific distribution. The VIX exhibits a historically inverse relationship with the , rising during periods of market stress such as financial crises, while declining in stable conditions, which underscores its role as a of market uncertainty. Investors utilize the VIX for , hedging against downside , and speculative trading; related products like VIX futures (launched in ) and VIX options (introduced in ) enable direct exposure to volatility dynamics on the Cboe and Cboe Options . Its mean-reverting nature and term structure further inform strategies for and diversification beyond traditional .

Fundamentals

Definition and Purpose

The CBOE Volatility Index (VIX) is a that represents the market's expectation of 30-day forward-looking in the , derived from the prices of options. It provides a standardized measure of anticipated price fluctuations in the underlying over the near term. At its core, the VIX is based on , which is the market's forecast of an asset's potential price movement as inferred from the premiums of its options contracts. reflects investor expectations embedded in option pricing, where higher premiums indicate greater anticipated swings in the asset's value. The VIX aggregates this specifically from a portfolio of [S&P 500](/page/S&P 500) options to yield a forward-looking estimate. The primary purpose of the VIX is to serve as a of sentiment regarding , often referred to as the "fear gauge" due to its tendency to rise during periods of heightened . High VIX values signal elevated levels of fear or market stress, suggesting expectations of significant , while low values indicate complacency and relative stability. VIX levels are expressed as annualized percentages; for instance, a reading of 20 implies an expected annualized of 20% for the over the next 30 days.

Specifications

The VIX index is constructed using the prices of out-of-the-money (OTM) put and call options on the Index (SPX), specifically those with strikes below and above the at-the-money level, respectively. These option prices are derived from the bid-ask midpoints to ensure a fair representation of market consensus, excluding any options with zero bid prices to focus on actively traded contracts. The index targets a constant 30-day maturity horizon, achieved by selecting near-term options with 23 to 37 days remaining until expiration and interpolating with the next-term options to precisely align with 30 calendar days. Time to expiration is calculated in calendar days but refined to minute-level precision for accuracy in the weighting process, ensuring the measure reflects a standardized forward-looking period. Discounting future cash flows in the calculation incorporates the U.S. Treasury , which provides the risk-free rates matched to the option maturities via cubic for smooth estimation. Only European-style SPX options are included, as they preclude early exercise and align with the index's assumptions; American-style options are excluded to maintain consistency. Dividends are not directly input but are implicitly accounted for through the option prices, which embed expectations of future payouts via put-call parity. The methodology was finalized in a 2003 white paper developed by the (CBOE) in collaboration with , establishing the current framework without major revisions since implementation. The VIX is computed in real time every 15 seconds during CBOE's trading hours, using filtered mid-quote data to produce an up-to-the-minute estimate of expected volatility.

Calculation

Methodology

The methodology for computing the VIX Index involves a systematic process to select and process (SPX) options, ensuring an accurate estimate of expected 30-day volatility through replication of a . This approach aggregates weighted prices of out-of-the-money (OTM) options to derive a market-based measure of variance, targeting a constant 30-day horizon as specified in the index parameters. Since October 2014, the methodology incorporates PM-settled SPX Weeklys (SPXW) options to better align with the 30-day target, excluding series expiring concurrently with AM SPX options. Option selection begins by identifying the at-the-money () strike as the one minimizing the between the call and put prices. The forward level F is then computed using this ATM strike: F = KATM + erT (C - P), where C and P are the prices at KATM. Next, K0 is determined as the highest less than or equal to F. From there, all OTM put options with strikes below K0 and OTM call options with strikes above K0 are included, starting from the strikes immediately adjacent to K0. Only options with non-zero bid prices are considered, and inclusion stops for puts or calls once two consecutive strikes exhibit zero bids, preventing the use of illiquid or unreliable quotes. This selection applies to both near-term and next-term expiration cycles, typically spanning 23 to 37 days to expiration, using AM-settled SPX options and PM-settled SPXW options (excluding those expiring on the same date as AM-settled SPX options) for standard calculations. To approximate a continuous of strikes and replicate the payoff of a , selected options are weighted inversely proportional to the between adjacent strikes (ΔK). The further incorporates the option's and an square of the , ensuring that contributions from lower and higher strike options reflect their relevance to overall variance estimation without overemphasizing sparse areas. This model-free replication draws from the theoretical framework of , where the is obtained by integrating option prices across strikes. For the time dimension, the blends options from the near-term and next-term expirations using weights based on their time to expiration (T₁ and T₂). Specifically, the total variance estimate for the constant 30-day maturity is interpolated as (T₂ - T_cm) (σ₁² T₁) + (T_cm - T₁) (σ₂² T₂) / (T₂ - T₁), where T_cm = 30/365 years, then the annualized variance σ² = interpolated total variance / T_cm, achieving a 30-day constant maturity regardless of the exact expiration dates available. If one expiration lacks sufficient options, the calculation defaults to the available term to maintain . Equivalently, calculations use minutes to expiration for : M_cm = 43,200 (30 days × 24 hours × 60 minutes), M_365 = 525,600. Data cleaning is integral to ensure reliability and avoid opportunities. Options with zero bids, null quotes, or where the bid exceeds the ask are filtered out entirely. The forward price (F) is derived from the strike by adding the rate-adjusted difference between the call and put prices at that strike, confirming consistency with put-call . Post-2003 refinements, introduced in the current , enhanced handling of sparse strike distributions by tightening these filtering rules and enabling updates approximately four times per minute during regular trading hours, improving responsiveness to market dynamics.

Formula

The VIX index value is calculated as VIX = 100 \times \sqrt{\sigma^2}, where \sigma^2 is the computed annualized variance of the index. This expresses the expected as an annualized percentage, providing a market-implied measure of 30-day forward-looking . The variance \sigma^2 is derived from the prices of out-of-the-money (OTM) put and call options on the S&P 500 index using the following equation: \sigma^2 = \frac{2}{T} \sum_i \frac{\Delta K_i}{K_i^2} e^{rT} Q(K_i) - \frac{1}{T} \left[ \frac{F}{K_0} - 1 \right]^2 Here, \Delta K_i is the interval between consecutive strike prices K_i, Q(K_i) is the midpoint quote (average of bid and ask prices) for the option at strike K_i, r is the risk-free interest rate, F is the forward index level derived from the option prices, and K_0 is the highest strike price less than or equal to the forward level F. The summation \sum_i runs over all OTM puts for strikes below K_0 and OTM calls for strikes above K_0, with the forward level F calculated as the strike at which the call-put price difference equals the discounted strike difference, specifically F = K + e^{rT} (C(K) - P(K)) using the ATM strike K (minimizing |C - P|). The risk-free rate r is obtained from U.S. Treasury yields via a cubic spline interpolation and converted from annual percentage yield to a continuously compounded rate. This formula originates from a model-free approach to replicate the payoff of a using a of OTM options, where the weights are proportional to $1/K_i^2 to match the of log returns under the . Although it assumes lognormal dynamics in the underlying derivation, the method is distribution-independent and relies solely on option prices, avoiding assumptions about the process. In practice, the VIX is computed in during trading hours using near-term (typically 23-37 days to expiration) and next-term options, with interpolation to achieve a constant 30-day maturity. The annualized variance is σ² = { (T₂ - T_cm) (σ₁² T₁) + (T_cm - T₁) (σ₂² T₂) } / { (T₂ - T₁) T_cm }, where T_cm = 30/365, T₁ and T₂ are times to expiration in years for near- and next-term, and σ₁², σ₂² are the term variances; then VIX = 100 × √σ². For precision, times are measured in minutes as per CBOE . For illustration, consider hypothetical options expiring in 30 days with a forward level F = 4000, r = 0.02, and selected strikes around K_0 = 3950: puts at strikes 3900 ($50 premium), 3950 ($30), and calls at 4050 ($40), 4100 ($20), with \Delta K_i = 50. The first term sums contributions like \frac{50}{3900^2} e^{0.02 \times 30/365} \times 50 \approx 8.3 \times 10^{-7}, aggregated across terms to yield \sigma^2 \approx 0.04, resulting in VIX \approx 20. This example assumes basic familiarity with option chains and demonstrates how option prices directly influence the variance estimate without requiring a specific model.

History

Origins and Development

The concept of a volatility index originated in academic research during the late 1980s, with Menachem Brenner and Dan Galai proposing the creation of such instruments to hedge changes in volatility using option prices as a measure of expected volatility. In their 1989 paper, they argued that a volatility , analogous to stock market indices, could be constructed from the implied volatilities derived from option premiums, providing a standardized benchmark for market expectations of future volatility fluctuations. This foundational idea built on the Black-Scholes model, which introduced implied volatility as a forward-looking estimate extracted from option prices, enabling the quantification of market-anticipated risk beyond historical realizations. Early proposals for implementing a practical volatility index emerged in discussions at the (CBOE) around 1991-1992, where researchers explored adapting concepts to create a tradable measure. Robert Whaley, a professor at , was commissioned by the CBOE to develop this index, drawing on extensive analysis of option data to formalize its structure. The CBOE played a central role in standardizing the approach, aiming to provide investors with a reliable gauge of equity market derived from option market dynamics. The initial methodology for the VIX, launched in 1993, relied on at-the-money options from the Index (OEX) to estimate 30-day expected volatility, focusing on a limited set of strikes to approximate under the Black-Scholes framework. This approach, while innovative, was constrained by its dependence on model assumptions and narrow option selection. In 2003, the CBOE collaborated with academic and industry experts to shift to a , incorporating a broader range of (SPX) out-of-the-money puts and calls for a more comprehensive replication, enhancing accuracy and replicability. Post-2021 academic critiques have highlighted ongoing limitations in the VIX methodology, particularly its challenges in capturing and heavy-tailed distributions prevalent in financial returns, which can lead to underestimation of tail risks during extreme events. Researchers have proposed extensions, such as regime-switching models, to address these gaps by better integrating non-normal dynamics observed in empirical data.

Key Milestones

The Cboe Volatility Index (VIX) was introduced on January 19, 1993, by the (CBOE), marking the launch of the world's first volatility index designed to measure market expectations of near-term conveyed by Index option prices. This initial version, based on options, provided real-time publication of as a benchmark for investors. On September 22, 2003, the CBOE updated the VIX methodology in collaboration with , shifting to a model-free approach using a wider range of (SPX) options to derive a more robust measure of 30-day expected . This revision, which back-calculated historical values to 1990, enhanced the index's accuracy and applicability, replacing the original S&P 100-based calculation and establishing the framework still in use today. Trading in VIX derivatives expanded significantly in the mid-2000s. VIX futures were launched on March 26, 2004, on the CBOE Futures Exchange (CFE), enabling direct exposure to expectations with 449 contracts traded on the debut day. This was followed by the introduction of VIX options on February 24, 2006, which quickly became one of the exchange's most successful products, allowing options strategies on itself. The VIX has reached notable peaks during periods of market stress. It hit an intraday record high of 89.53 on October 24, 2008, amid the global financial crisis, reflecting extreme uncertainty in equity markets. During the , the index closed at a record 82.69 on March 16, 2020, surpassing prior highs as lockdowns triggered widespread sell-offs. More recently, on August 5, 2024, the VIX experienced its largest one-day percentage spike, surging 180% to an intraday high of 65.73 due to global market turmoil. In 2025, the VIX again demonstrated its sensitivity to geopolitical risks, spiking above 60 in early April amid escalating U.S.- tensions that led to a 7% drop in the on April 4. In October 2025, the VIX surged approximately 37% to an intraday high of 22.44 on October 10 amid renewed U.S.- tariff threats and market sell-offs. Regulatory scrutiny of VIX-related operations occurred in May 2021, when the U.S. imposed a $9 million penalty on for undisclosed errors in VIX calculations during the February 5, 2018, volatility surge, highlighting the need for robust in index computation. The CBOE continues to monitor and refine VIX operations under ongoing regulatory oversight to ensure reliability.

Interpretation

Market Implications

The VIX serves as a key barometer of , with its levels providing insights into investor expectations of future in the S&P 500. Generally, a VIX reading below 20 signals low expected and market complacency, indicating a stable environment where investors anticipate minimal fluctuations. Levels between 20 and 30 suggest moderate uncertainty, often accompanying rising concerns about economic or geopolitical events, while readings above 30 reflect heightened and potential for significant market swings. Extreme spikes exceeding 80, as observed during major crises, underscore acute and uncertainty among investors. The VIX exhibits a strong inverse with the S&P 500, typically rising when stock prices fall and vice versa, with historical daily percentage change around -0.70. This relationship stems from the VIX's role in capturing investor demand for protective options during equity downturns. Additionally, the VIX demonstrates a mean-reverting tendency, fluctuating around a long-term of approximately 19-20, which influences trading strategies and futures term structures as volatility extremes tend to subside over time. From a perspective, elevated VIX levels amplify risk-averse behaviors, such as and selling, exacerbating anomalies like overreactions to news. As a forward-looking measure, the VIX quantifies expected 30-day derived from options prices, rather than past realized , offering limited predictive power for market direction but valuable for assessing risk premiums and . Investors often use high VIX readings to portfolios by purchasing volatility-linked instruments, which gain value during downturns to offset losses. Conversely, VIX spikes can serve as signals, prompting buys in stocks as excessive fear may indicate oversold conditions and potential rebounds. Inverse ETFs, such as those shorting VIX futures, exhibit positive correlations with the , providing leveraged exposure to calm markets but amplifying losses during surges. In recent contexts, the VIX's spike to over 65 on , , amid global economic concerns and a weak U.S. , highlighted market vulnerabilities and prompted rapid hedging activity, though it was later viewed as an overreaction with quick reversion. Similar spikes occurred in December (reaching 28.32) and April 2025, highlighting persistent vulnerabilities to specific events. Throughout 2025, the VIX has fluctuated around 18-20, with levels near 20 in late 2025 amid ongoing market uncertainties, consistent with its long-term average.

Limitations

The VIX Index, while widely regarded as a measure of expected market , is fundamentally non-predictive of future realized , as it reflects current prices of options rather than actual future market movements. Empirical analyses demonstrate that the VIX exhibits poor timing accuracy for market turns, often failing to anticipate spikes or declines effectively. For instance, during non-crisis periods, it systematically overestimates realized by approximately 430 basis points across various horizons, leading to misguided assessments. Biases in the VIX arise from supply and demand imbalances in the underlying options market, particularly hedging demand from investors seeking protection against tail risks, which can inflate implied volatility levels. The index assumes a constant 30-day maturity and European-style options without incorporating sudden jumps in asset prices, potentially distorting its representation during turbulent conditions. Additionally, the VIX's reliance on a model-free methodology overlooks extreme events, limiting its ability to fully capture tail risks beyond normal market fluctuations. Coverage limitations further constrain the VIX's applicability, as it is derived exclusively from S&P 500 (SPX) options, focusing solely on U.S. large-cap equities and excluding broader global or sector-specific volatilities. This U.S.-centric scope renders it less relevant for international markets or smaller-cap segments, where volatility dynamics may differ significantly. Academic studies following the 2008 financial crisis have highlighted the VIX's tendency to overestimate volatility during calm periods, with biases reaching up to 485 basis points in bull markets, while underestimating it amid crises like the 2008 downturn by around 180 basis points. In 2021, the U.S. Securities and Exchange Commission (SEC) charged S&P Dow Jones Indices with failures in VIX futures index calculations, revealing vulnerabilities such as an undisclosed "Auto Hold" feature that froze values during a 115% VIX spike on February 5, 2018, resulting in stale data and overstated indicative values for related products. As an alternative, realized volatility measures derived from GARCH models often outperform the VIX in forecasting accuracy, particularly out-of-sample, by better incorporating historical data and volatility shocks under the physical measure, with lower errors (e.g., 2.870 vs. higher for VIX-based approaches). Recent from 2023 to 2025 on the VIX1D Index, launched by Cboe in 2023, addresses intraday limitations of the original VIX by incorporating zero-days-to-expiration (0DTE) SPX options to measure expected over the current . Studies show that while the VIX1D overestimates intraday by about 36%, adjustments using a realized risk premium proxy improve one-day forecasts, achieving up to 30% better performance compared to traditional models and 77.85% directional accuracy based on data through August 2024.

Trading and Products

Derivatives

VIX derivatives primarily consist of futures and options contracts that allow investors to trade and expected volatility in the Index directly. These instruments, traded on the Cboe Futures Exchange (CFE) and Cboe Options Exchange, provide exposure to the VIX Index without requiring ownership of the underlying options used in its . VIX futures contracts, introduced in on the CFE, settle in to the value of the VIX Index at expiration and serve as the primary vehicle for trading near-term expectations. These contracts include standard monthly expirations, weekly contracts (introduced in 2015 with up to six consecutive weekly series), and end-of-month variants, enabling precise timing for strategies. The futures curve often exhibits , where longer-dated contracts trade at a to nearer-term ones, resulting in negative roll for holders of long positions as they roll contracts forward; conversely, backwardation occurs during periods of market stress, with nearer-term futures at a , potentially generating positive roll but signaling heightened short-term . VIX options, launched in 2006 on the Cboe Options Exchange, are European-style contracts exercisable only at expiration and are available on both the VIX Index and VIX futures. They enable investors to volatility exposure by buying puts to protect against rising or calls to speculate on increases, independent of directional market moves. These options expand hedging capabilities beyond futures by offering prices and expiration flexibility for tailored . To accommodate smaller investors, mini VIX futures and options were introduced, with mini futures launching in August 2020 at one-tenth the size of standard contracts (multiplier of $100 versus $1,000). These mini products lower the capital requirements for trading, facilitating broader participation in hedging or speculative strategies while maintaining the same mechanics as their standard counterparts. VIX options followed, providing similar scaled-down exposure to VIX futures. All VIX derivatives are cash-settled based on the Special Opening Quotation (SOQ) of the VIX Index, calculated on the morning of expiration (typically a Wednesday) using the opening prices of a specific portfolio of options. This process mirrors the settlement of A.M.-settled options, ensuring consistency and reducing basis risk between the index and . VIX exhibit high , with trading volumes surging during crises; for instance, the August 2024 volatility spike saw the VIX reach over 65 intraday, driving record futures and options activity amid global equity selloffs. In 2024, the launch of options on VIX futures in October enhanced accessibility, allowing direct positioning on futures curves via Cboe's platforms. By October 2025, overall Cboe options volume, including VIX-related products, hit a monthly average daily volume record of 21.4 million contracts, reflecting sustained amid ongoing uncertainty.

Exchange-Traded Products

Exchange-traded products (ETPs) linked to the VIX allow investors to gain exposure to expected market volatility without directly trading VIX futures or options. These include exchange-traded funds (ETFs) and exchange-traded notes (ETNs), which primarily track VIX futures indices rather than the spot VIX level. The inaugural VIX-linked ETN, the iPath VIX Short-Term Futures ETN (), was launched by on January 29, 2009, providing a for hedging against equity market declines. This development followed the , during which volatility surged and interest in VIX-based instruments grew substantially, leading to increased issuance and trading volumes of such products through 2009. Most VIX ETPs track the VIX Short-Term Futures Index, which maintains to the first- and second-month VIX futures contracts through a daily rolling process to replicate a continuously rolling position. Prominent examples include , which offers long to short-term VIX futures, and the VelocityShares Daily Inverse VIX Short-Term ETN (XIV), an inverse product that provided short until its discontinuation in February 2018 following extreme market . These products cater to and institutional investors seeking tactical bets, with remaining one of the most liquid VIX ETPs. Leveraged VIX ETPs amplify daily returns of underlying futures indices, such as the 2x Long VIX Futures (UVIX) from Volatility Shares, which targets twice the performance of short-term VIX futures. However, these leveraged vehicles are prone to significant decay from daily rebalancing and the costs of rolling futures contracts, particularly in environments where longer-dated futures trade at a to near-term ones. For instance, UVIX experienced magnified gains during spikes, such as a 25-31% VIX surge in October 2025, but has shown accelerated long-term erosion, underperforming 2x the index over extended holding periods due to effects and roll costs. A key risk of VIX ETPs is their tendency for long-term underperformance relative to the spot VIX, driven by negative roll yield in persistent contango, which accounts for over 70% of the VIX futures curve's state historically. This structural feature results in gradual value erosion for long ETPs like VXX, even if the VIX remains stable, as the daily roll from higher-priced longer-dated contracts to lower-priced near-term ones generates losses. Inverse and leveraged variants exacerbate this decay through leverage resets, making them unsuitable for buy-and-hold strategies and better suited for short-term trading. Additionally, these products do not offer direct spot VIX exposure, limiting their utility as pure volatility hedges. Regulatory oversight by the U.S. has shaped the evolution of VIX ETPs, with approvals for new listings accelerating from 2021 onward amid rising demand for volatility tools. In 2022, the SEC greenlit UVIX and similar 2x products, while 2025 saw filings for 3x and 5x leveraged ETFs from issuers like Volatility Shares (primarily for single stocks and cryptocurrencies), though approvals remain pending due to concerns over investor protection and market stability. The 2024 VIX spike, reaching intraday highs above 65 amid weak economic data and market turmoil, drove record trading volumes in existing ETPs, highlighting their role in crisis periods but also prompting SEC scrutiny of leveraged exposures. Through mid-2025, VIX ETP exceeded $5 billion, reflecting sustained growth despite inherent risks.
ProductTypeIssuerLaunch YearKey Feature
VXXLong ETN iPath2009Tracks VIX Short-Term Futures Index
XIVInverse ETN (VelocityShares)2011-1x short-term VIX futures (discontinued 2018)
UVIX2x Long Volatility Shares2022Leveraged exposure to short-term VIX futures

Advanced Concepts

Volatility of Volatility

The VVIX, formally known as the CBOE VIX of VIX Index, measures the expected 30-day of the VIX Index, derived from the prices of a portfolio of out-of-the-money VIX options. This metric captures the market's anticipation of fluctuations in itself, often termed the volatility of volatility (vol-of-vol). The VVIX employs a calculation methodology analogous to the VIX but applied specifically to VIX options, interpolating values from options expiring approximately 30 days forward. Introduced by the CBOE on March 14, 2012, it provides a for assessing the embedded in VIX option prices. Elevated VVIX levels signal heightened uncertainty regarding near-term expectations, reflecting second-order risks in markets. It typically fluctuates in the range of 80 to 150, with a historical around 86, though it exhibits greater than the VIX due to its focus on volatility dynamics. For instance, the VVIX spiked sharply during the 2020 market turmoil, underscoring amplified vol-of-vol amid global economic disruptions. In contrast to the VIX, which averages around 20 and rarely exceeds 40 in calm periods, the VVIX maintains consistently higher readings and displays more pronounced , aiding traders in evaluating tail risks and hedging strategies involving VIX . The CBOE Volatility Index (VIX) family includes several variants designed to measure expected over different time horizons using options on the (SPX), enabling investors to gauge tailored to specific durations beyond the standard 30-day period. These include the VIX9D Index for 9-day , VIX3M for 3-month , and VIX6M for 6-month , each calculated similarly to the VIX but incorporating options with corresponding maturities to reflect shorter or longer forward-looking expectations. A notable recent addition is the CBOE 1-Day Volatility Index (VIX1D), launched on April 24, 2023, which measures the market's expectation of volatility over the current trading day using near-term SPX options. The VIX1D addresses limitations in traditional measures by focusing on intraday , though its introduces an overnight bias, causing the index to typically rise during regular trading hours and decline overnight due to unequal of trading versus non-trading periods. Research demonstrates that the VIX1D enhances short-term predictions; for instance, an adjusted version of the index outperforms standard models like the Heterogeneous Autoregressive (HAR) model in forecasting next-day realized , achieving approximately 30% better accuracy in some evaluations from 2024-2025 studies. This makes the VIX1D particularly useful for strategies, such as those involving zero-days-to-expiration (0DTE) options, where rapid intraday sentiment shifts are critical. Shorter-term variants like the VIX1D and VIX9D tend to be more reactive to immediate market events and news compared to the 30-day VIX, which provides a smoother, forward-looking view less influenced by transient shocks. On days of elevated volatility, these indices capture acute short-term impacts more acutely, while longer-horizon ones like VIX3M and VIX6M offer stability for assessing sustained risk. Internationally, analogous indices exist, such as the VSTOXX, which measures 30-day for the Index using options on European blue-chip stocks, serving as the primary gauge of equity market fear similar to the VIX. These extensions collectively allow for customized assessments across regions and time frames, supporting diverse and trading applications.

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