The volatility smile

Option markets contain much information about market perceptions that asset
returns are not normal. Earlier we discussed the differences between the actual
behavior of asset returns and the random walk hypothesis which underlies the
Black–Scholes option pricing model. The relationship between in- or out-of-the money
option prices and those of at-the-money options contains a great deal of information
about the market perception of the likelihood of large changes, or changes in a
particular direction, in the cash price.
The two phenomena of curvature and skewness generally are both present in the
volatility smile, as in the case depicted in Figure 1.21. The chart tells us that options
which pay off if asset prices fall by a given amount are more highly valued than
options which pay off if asset prices rise. That could be due to a strong market view
that asset prices are more likely to fall than to rise; it could also be due in part to
market participants seeking to protect themselves against losses from falling rates
or losses in other markets associated with falling rates. The market is seeking to
protect itself particularly against falling rather than rising rates. Also, the market is
willing to pay a premium for option protection against large price changes in either
direction.
Different asset classes have different characteristic volatility smiles. In some
markets, the typical pattern is highly persistent. For example, the negatively sloping
smile for S&P 500 futures options illustrated in Figure 1.22 has been a virtually permanent feature of US equity index options since October 1987, reflecting market
eagerness to protect against a sharp decline in US equity prices. In contrast, the
volatility smiles of many currency pairs such as dollar–mark have been skewed,
depending on market conditions, against either the mark or the dollar.