{"id":18764,"date":"2026-06-28T21:19:52","date_gmt":"2026-06-28T21:19:52","guid":{"rendered":"https:\/\/www.simtrade.fr\/blog_simtrade\/?p=18764"},"modified":"2026-06-28T22:00:11","modified_gmt":"2026-06-28T22:00:11","slug":"cboe-volatility-index","status":"publish","type":"post","link":"https:\/\/www.simtrade.fr\/blog_simtrade\/cboe-volatility-index\/","title":{"rendered":"CBOE Volatility Index"},"content":{"rendered":"\n\"Saral<\/a>\n\n

In this article, Saral BINDAL<\/a> (Indian Institute of Technology Kharagpur, Metallurgical and Materials Engineering, 2024-2028 & Research assistant at ESSEC Business School) explains the CBOE methodology for the construction of the volatility index or \u2018VIX\u2019.<\/p>\n\n\n

Introduction<\/h2>\n\n

The Chicago Board Options Exchange (CBOE) Volatility Index, or VIX, is a real-time market index designed to measure the market\u2019s expectation of 30-day forward-looking annualized volatility. It is option-based, calculated using the market prices of S&P 500 index options to gauge expected volatility.<\/p>\n\n\n

History<\/h2>\n\n

In 1993, CBOE Global Markets introduced the CBOE Volatility Index (VIX Index). Originally designed by Robert E. Whaley (1993) to measure the market\u2019s expectation of 30-day volatility, the index was calculated using an option-pricing model to derive the implied volatility of at-the-money S&P 100 index (OEX Index) options. The VIX Index quickly became the premier benchmark for U.S. stock market volatility and is widely referred to as the market’s “fear gauge”.<\/p>\n\n

Ten years later in 2003, CBOE partnered with Goldman Sachs to completely overhaul the index. This update introduced a methodology independent of option-pricing models, adapting the seminal theoretical framework for model-free implied variance established by Britten-Jones and Neuberger (2000) alongside the practical replication insights of Demeterfi et al. (1999). This modern version of the VIX shifted its underlying base to the broader S&P 500 index. Rather than tracking a narrow selection of options, it estimates market expectations by aggregating a heavily weighted cross-section of SPX puts and calls across a wide range of strike prices.<\/p>\n\n

Academic research confirms that this model-free aggregation method captures more information and provides a more efficient forecast of future realized volatility than individual Black-Scholes implied volatilities (Jiang & Tian, 2005).<\/p>\n\n\n

Market Behavior<\/h3>\n\n

While VIX is often regarded as the market\u2019s fear<\/i> index, it might give one a false impression that it moves opposite to the S&P 500. Mathematically it has no directional bias, and only measures the magnitude of expected volatility. Instead, the real-world inverse relationship is driven by corporate capital structures and asymmetric investor behavior. As Black (1976) pointed out, when a stock price drops, a company’s financial leverage automatically increases, making the equity riskier and naturally driving up volatility.<\/p>\n\n

Furthermore, market sell-offs trigger a sudden panic where investors rush to buy portfolio insurance (put options) all at once. Because the supply of this insurance is limited, options market makers must aggressively raise prices to protect themselves. G\u00e2rleanu et al. (2009) formalize this mechanism, demonstrating that because market makers cannot perfectly hedge their positions, concentrated investor demand directly drives option pricing and inflates implied volatility premiums. Since the VIX is calculated directly from these option prices, this demand-pressure mechanically forces the index to spike.<\/p>\n\n

This same demand explains why the S&P 500 and the VIX occasionally rise together. During massive market rallies, investors experience FOMO (Fear of Missing Out) and rush to buy upside call options, or quickly buy puts to lock in their rapid gains. Just like during a market crash, this sudden increase in demand for options overwhelms market makers. To protect themselves, they hike option prices, which mechanically forces the VIX up even as the stock market climbs.<\/p>\n\n\n

Option Selection Procedure<\/h2>\n\n

Selecting Eligible Expiration Dates<\/h3>\n\n

The VIX is designed to measure the market’s expectation of volatility over the next 30 calendar days. However, listed S&P 500 options rarely expire exactly 30 days from the calculation date. To address this, the methodology selects two option maturities: a near-term<\/b> maturity of less than 30 days and a next-term<\/b> maturity of more than 30 days remaining. Variance estimates are calculated for both maturities and subsequently interpolated to obtain a constant 30-day measure of expected volatility.<\/p>\n\n

In the CBOE volatility index calculation methodology, time to expiration of a constituent option series, is calculated by dividing the number of minutes until expiration (MTime to Expiry<\/sub><\/i>) of the selected options (rounded down to the nearest minute) by the number of minutes in a year (M365<\/sub><\/i>).<\/p>\n\n


\n<\/p>\n\n\n

Estimating the Forward Index Level<\/h3>\n\n

The next step is to estimate the forward index level of the S&P 500 using option markets prices. It represents the market’s expectation of the index value at expiration under the risk-neutral measure and serves as the reference point for selecting the relevant option contracts used in the calculation.<\/p>\n\n

It is calculated using the principle of put-call parity, specifically by finding the unique strike price where the price difference between the call and the put option is at its absolute minimum.<\/p>\n\n


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Where:<\/p>\n