Volatility surface is defined as a three-structural plot of stock option implied volatility perceived to surface because of inconsistencies in prices of stock options and pricing models indicating the right prices. Before explaining this matter further, let us understand the fundamentals of stock options and stock option pricing.

Stock option is a privilege where the holder has the right, not the obligation, to trade the stock at a predetermined price within a specific time period. A call option allows the owner to buy the underlying stock at the strike price on or before its maturity. Conversely, a put option enables the holder to sell the underlying stock at the strike price on or before its expiration date.

Basically there are two types of options. An American option can be exercised on or before maturity. A European option, on the other hand, can be executed only on its expiration date. Other kinds of option exist as well, including Bermudan options.

In 1973, Fischer Black, Robert Merton, and Myron Scholes designed the Black Scholes model. It is anchored in six presumptions.

  • Interest rates are consistent.

  • The option must be European-style.

  • No commissions are levied on trades.

  • Financial markets are effective.

  • Returns of the underlying stock are log-normally disbursed.

  • The underlying stock will never give dividend payments.

The following factors are accounted to assimilate the option price: current market price, strike price, interest rate, time until maturity, and volatility. Aside from these variables, the cumulative standard normal distribution and the mathematical constant "e," which is equivalent to 2.7183, are integrated in the computation.

Volatility is the sole variable that is not certain in the formula for option pricing. Going back to its definition, volatility surface is a three-faceted plot in which the x-axis pertains to the expiration date, y-axis is the projected volatility, and z-axis is the selling price. This illustration, which is far from flat, differs through time since the stipulations of the Black Scholes model are not always correct. Nevertheless, majority of financial institutions rely on this model.