Stock options come in two types: call options and put options. The Black-Scholes model is used to value options, with implied volatility being the only unknown input. Options pricing must also consider market realities such as dividends and interest rates. Pricing options for strike prices far away from the current price of the underlying results in a “volatility smile”.
Stock options come in two varieties. A call option is the right to buy a certain asset at a fixed price by a specific date. A put option is the right to sell a particular asset at a fixed price by a specific date. The asset to be bought or sold is called the underlying, strike price or strike price, is the price at which the underlying will be bought or sold, and the expiration date is the time when the option can no longer be exercised.
Options are usually valued using the Black-Scholes model. It combines the time remaining to expiration, the strike price, the current price of the underlying, and an estimate of future volatility known as implied volatility (IV) to generate a theoretical price for an option.
Since implied volatility is the only unknown input, correct option pricing depends entirely on accurate predictions of future volatility. The usual approach is to measure the actual volatility of the underlying in the recent past, adjust for anticipated news events such as an upcoming earnings release, and add some margin of safety. This approach works quite well for liquid (heavily traded) options.
Pricing options for strike prices far away from the current price of the underlying is a bit more complicated. Partly as a reflection of their lower liquidity and partly as an acknowledgment that unexpected large price movements can and do occur, such options have an extra layer of margin added to their price.
This results in something referred to as the “volatility smile”. Black Scholes can be used in reverse to calculate the implied volatility (IV) needed to generate a given price; graphing the IV for a broad range of strike prices will result in a smile-like plot. That is, the further the strike price is from the underlying price, the higher the IV.
The pricing of options must also take into account some other market realities. If the underlying pays dividends and one is payable before maturity, the pricing model must take this into account. The price of options is also sensitive to interest rates; if the overall economic situation is one in which interest rates are likely to move significantly in the foreseeable future, adjustments will be needed.
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