The basic idea behind skew is that options with different strike prices and different expirations tend to trade at different implied volatilities. When we plot implied volatilities for options with the same expiration, the graph resembles a smile, with at-the-money volatility in the middle and out-of-the-money options forming the gently rising sides. As options go into-the-money, they gradually approach their intrinsic value, and an option trading at its intrinsic value has an implied volatility of zero. Therefore, for our graph, we use call prices for strikes above the current underlying stock price and put prices for strikes below the current underlying stock price.

There is a mathematical reason that skew appears as the volatility smile described above. Most option pricing models assume stock prices are log-normally distributed, but in the real world, stock prices deviate slightly from that model. Specifically, the normal distribution underestimates the probability of extremely large moves. In order to compensate, traders 'tweak' their models by using a higher volatility for out-of-money options.

However, the skew also holds valuable information. An investor who takes the time and effort to analyze the skew of a stock’s options can gain important insights into how the market is pricing risk. In some cases, for example, the perceived downside risk may be greater than the perceived upside risk, which causes the graph to be more of a smirk than a smile.