Volatility skews and smiles are empirical observations of the implied volatility, according to Black-Scholes, as a function of strike price. The implied volatility is the volatility parameter we would need to plug into Black-Scholes to obtain the market price of an option. $$ $$ If we determine the implied volatility of options with the same time to expiry, but different strikes, then we often obtain a curve that resembles a smile or a skew, where implied volatility increases for options far out of the money. There are many explanations for this phenomenon. One is that market returns exhibit 'fat-tails', and the market expects large deviations in market price more frequently than the lognormal model underlying Black-Scholes would predict. As a result, options that are well out of the money are priced higher than Black-Scholes would predict, since Black-Scholes underestimates the likelihood of those options expiring in the money. This in turn gives higher implied volatilities at the extremes and results in a volatility smile. $$ $$ Whereas volatility smiles are roughly symmetric about the current spot price, volatility smirks are skewed preferentially towards one side, with either call or put options being highly priced by the market. This is often an asset-specific phenomenon - risky assets such as stocks can often exhibit a negative skew, with out of the money put options being priced highly. This is because the downside risk of stocks is generally greater than the upside risk - a company can go bankrupt or be involved in a scandal for example, whereas there are not many events that can cause a stock to shoot up in price. Traders will therefore tend to purchase more out of the money put options as insurance. Commodities however are more likely to exhibit a positive skew - not many factors can cause a commodity price to drop significantly, however supply chain issues caused by geopolitical events can create a shortage of a commodity resulting in a rapid price increase. Traders are more likely to buy out of the money call options as insurance, increasing their price.