VIX, volatility and implied volatility

What is the concept of volatility?

Volatility is the degree to which the price of a stock or other financial instrument fluctuates over a period of time. Its value is usually determined based on the standard deviation of price changes. For stocks that are considered stable - for example, Coca-Cola shares - volatility is relatively low. Price changes in these stocks are minimal and their value is relatively stable. In contrast, the shares of Tesla, a company involved in the production of electric cars, show significantly more dynamic price movements. It is clear that the volatility of Tesla shares is higher than that of Coca-Cola shares.

The volatility of a stock or index can be expressed as an annual percentage. Before discussing volatility in more detail, it is important to understand how we should interpret volatility as a percentage.
For the purposes of options investors, it is essential to distinguish between two types of volatility - historical volatility and expected volatility.

Historical volatility refers to fluctuations in the price of a financial instrument based on its past performance, while expected volatility represents the future volatility of the instrument as predicted by the market based on the valuation of its derivatives (in particular options).

If an underlying asset has an expected volatility of 24 %, this means that the market expects an annual volatility of 24 % for that asset. To convert the volatility on a daily basis, the expected volatility must be divided by 16, which corresponds to the square root of the number of trading days in a year.

Most models for options assume 252 trading days per year. For simplicity, we use a slightly inflated value to avoid rounding complications. So an expected volatility of 24% on an annual basis corresponds to a daily volatility of 1.5% (= 24% / 16). If the expected volatility were 48%, the daily volatility would be 3%. Higher volatility means more price volatility. Now let's take a closer look at both types of volatility.

Historical volatility

Historical volatility refers to the actual price movements of a stock or index in the past. It is calculated based on the standard deviations of daily results over a 30-day period. Historical volatility thus shows how prices have evolved in the past.

In quiet periods, when daily market movements are minimal, volatility decreases. There is a negative correlation between volatility and market direction. In periods of falling markets, volatility is higher than in periods of rising markets.

Understanding implied volatility

Implied volatility offers insight into the market's expectations of future stock or index prices and is based on current supply and demand for options, thereby reflecting predictions of market sentiment. Unlike backward-looking historical volatility, implied volatility is constantly changing and adjusting in response to changes in supply and demand in the options market. For example, strong demand for put options may signal an increase in implied volatility and a rise in the prices of those options. External factors such as economic news or unexpected events may periodically cause it to rise or fall.

Changes in implied and historical volatility have a similar effect on price movements. In times of financial uncertainty, if markets fall, implied volatility and option prices usually rise. Conversely, when markets stabilise and investor confidence returns, implied volatility falls, leading to lower option prices. This mechanism works in the same way as the historical volatility assessment and is reflected in the vega parameter, which shows how changes in volatility affect the option price.

The market dynamics are illustrated by two scenarios:

* If an investor buys a put option with the expectation that the price of the underlying asset will fall, the dual action of market forces increases the price of the option. Firstly, the negative delta will increase the value of the option and secondly, the increasing volatility caused by falling markets will further increase the price of the option due to rising vegetation.

* When buying a "call" option in anticipation of a rising stock market, the price of the option may increase due to a positive delta. However, if the market is rising and volatility is falling, the vega of the option will fall, which may have a negative effect on its price.

The VIX index, known as the "fear index," reflects the market's expectations of the volatility of the S&P 500 index. If volatility remains unchanged, the option may be sold at a lower price. It was introduced in 1993 by the Chicago Board Options Exchange (CBOE) and provides a measure of expected volatility based on data on the prices of options on the S&P 500 index. The CBOE began trading VIX futures contracts in 2004 and added options in 2006. Today, the VIX is an actively traded instrument that investors use to hedge or speculate on future market volatility. Its average value has hovered around 20 points over the past 15 years, but during the financial crisis and the collapse of investment bank Lehman Brothers, its value shot to all-time highs.