relying on any theoretical model of option pricing. The methodology provides an
approximate measure of stock market volatility from a hypothetical option with exercise
price equal to the futures price and with thirty days remaining to maturity. As such, the new
VIX index provides an estimation of a thirty-day return variance swap rate from a portfolio
of options spanning the nearest two maturities. The contribution of each option to the
implied volatility index is an increasing (decreasing) function of the exercise price for put
(call) options.4
The empirical analysis is based on the daily time-series of the implied volatility
indices for a sample period extending from January 1990 to December 2004, and spanning
180 options maturities. Figure 1 describes the behavior of spot prices and implied volatility
indices for the U.S. and Japanese markets. There is a tendency for the S&P 500 index to
increase monotonously until the burst of the information technology bubble. This pattern
contrasts with the tendency for Nikkei 225 index to decrease from its height in early 1990,
reflecting the persistent recession of the Japanese economy during the 1990s. Although
there appears a tendency for implied volatility across markets to converge in more recent
years, the Nikkei 225 implied volatility seems to remain typically higher than expectations
of US market volatility.
There are instances of sharp increases in implied volatility in both markets. The
occasional spikes in implied volatility tend to be associated with sharp decreases in stock
market prices. These events are seemingly associated with significant economic events such
4 The model-free methodology for the calculation of S&P 500 implied volatility index is
thoroughly explained in CBOE documentation. It follows the original VIX index based on
S&P100 American options calculated using Black-Scholes pricing model. The rationale
underlying the calculation of these indices and their major differences are discussed in
Carr and Wu (2006).
10
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