What is a Volatility Skew?

Volatility skew is a financial term that refers to the graph of implied volatility as a function of the strike price of an option. It is drawn by using market option prices to work backward in the Black-Scholes options pricing model to find the volatility of the underlying asset. The graph spans the available strike prices for both call and put options. It holds the underlying asset and the option expiration date constant. Investors have given names to common volatility skew shapes: a U-shaped graph is a volatility smile, a graph that shows higher volatility at lower prices is a volatility smirk or a reverse skew, and a graph that shows higher volatility at higher prices is a forward skew.

The Black-Scholes pricing model uses the volatility of an asset to predict the prices of options on that asset. It applies to both call and put options. Call options allow the holder to buy stock at a predetermined price, called the strike price, regardless of the market price of the stock. Put options allow the holder to sell the stock at the strike price.

An example can illustrate the Black-Scholes model. A stock sells today for 35. Tomorrow, it has a 50 percent chance of dropping to 20 and a 50 percent chance of rising to 50. A call option with a strike price of 30 that expires tomorrow will give a profit of zero in the first case and 20 in the second. Since each case has a 50 percent probability of occurring, the value of the option today is 10.

The example is highly simplified, allowing only two future states. Real-world option pricing uses probability functions to take into account the full distribution of potential future states. This simplified version, however, illustrates the logic behind option pricing.

Black-Scholes assumes that volatility is constant for the underlying asset across strike prices, which makes sense: even if two investors hold options with different strike prices, they will see the same reports coming from the stock exchange. The implied volatility, however, can vary, creating the volatility skew. Using the market price as the option price and reversing the Black-Scholes process above yields the volatility skew curve for an asset. The implied volatility should be constant, but it is not, implying that options are mispriced in real-world markets. The variation is caused by psychological factors that inflate demand at one end of the price spectrum.

High demand for an option drives up the price, which results in increased implied volatility of the asset. Options can be separated into classes by their strike prices. In-the-money options are options that investors could profit from if they could exercise them in the present. This means that call options with a strike price that is lower than market price and put options with a strike price that is higher than market price are in-the-money. Out-of-the-money options are the opposite, and at-the-money options have a strike price that is equal to the market price.

Demand varies across option classes, which creates the distinctive patterns of volatility skew graphs. The volatility smile pattern is common in the foreign exchange market, and it indicates that investors would rather hold in-the-money or out-of-the-money options than at-the-money options. A preference for one side of the graph produces a reverse or forward skew, and is caused by investors’ aversion to risk. For example, commodities markets have forward skews because out-of-the-money calls can protect investors from the dangers of delivery failure.