'Fear gauge' reflects market sentiment
The volatility of stock markets has increased since the early 1990s. This prompted the Chicago Board Options Exchange (CBOE) to work on a volatility index. The VIX Index was developed by the CBOE based on the volatility of a stock market index in 1993.
'The original idea for the VIX was that it would be like the Dow Jones or S&P Indices for stocks, but would tell us the level of the option market,' says Stephen Figlewski, professor of finance at the Leonard N Stern School of Business, New York University. 'Options are derivative securities. The value of options depends on the underlying asset. When the S&P 500 goes up, call options will go up but put options will go down. We need a measure on how options are priced relative to the stocks. That is the idea of the VIX.'
The CBOE modified the methodology for computing the VIX in 2003. A VIX futures contract was launched in 2004 and VIX options trading began in 2006. The CBOE now lists a number of volatility-related indices and derivative contracts based on them. VIX-type indices and derivatives are traded throughout Europe.
In option pricing theory, 'volatility' has a specific mathematical definition. It is the standard deviation, expressed as an annualised per cent, of the logarithmic return for some underlying asset, such as a stock, stock index or interest rates.
'This sounds very precise,' Figlewski says. 'When it comes to trading options, volatility has several meanings which are related concepts. To understand VIX requires the understanding of how the concepts fit together.'
Volatility is the size of a typical price move over a given interval, like a day's trading. Based on the calculation on the data of the Hang Seng Index up until November 26, the index moved on average about 300 points a day over the previous month, which on an annual basis corresponds to a volatility index of 21.3 per cent.
The 300 points a day is the standard deviation of one-day return. Most long-term investors focus on what will happen over a long period of time and the movements over longer terms, Figlewski adds. 'These investors need to consider how much uncertainty there is about what the index will be trading at some point in the future after a lot of the '300 points a day' days.'
Volatility can also come from either the 'true' (empirical or real world) probability distribution or the 'risk neutral' distribution. The empirical distribution describes what actually happens day-to-day or month-to-month on the Hang Seng Index.
The risk neutral distribution is a measure of how options are being priced in the market. 'It includes the market's idea about how big daily price fluctuation may be and also the market's risk appetite,' Figlewski says. 'The option prices can be high because the market does not like bearing risks.'
As for the relation between volatility and option pricing, the celebrated Black-Scholes option pricing model values an option as a function of five parameters: present stock price, option exercise price, time to expiration, interest rates and volatility.
The model is based on an arbitrage trade where one buys the options and then sells an equivalent amount of the underlying stock or vice versa. The proportions need to be rebalanced constantly until the option expiration day. 'In the theoretical world of Black-Scholes, there is no problem rebalancing all the time, which means that we can create a risk less position,' Figlewski says.
'The Black-Scholes model comes from the idea that we are trading all the time. So what matters is how much the market is actually moving over the very short run. The first volatility concept of how big a one-day move is the one we use in a theoretical option pricing model. But real-world investors can't trade all the time and make risk less positions. Therefore, option prices in the market also include the market's risk appetite.'
VIX is sometimes referred to as the 'fear gauge' because it also reflects the market sentiment. Figlewski says VIX is a combination of market sentiment and the market's estimate of what the actual volatility is. If the market (that does not like volatility) thinks the actual volatility is going to be 20, the risk neutral volatility will be higher, perhaps 25. 'That is the number that would be going into the option pricing formula. VIX not only reflects the market's expectation of what the actual price of stocks is going to be, it also shows how the market feels about their risk.'
