Real-World Option Pricing by Lawrence D. Cavanagh
Option models calculate premiums or the prices of options on the assumption that volatility is a constant. Here's how stock and index price changes are distributed in the real world and how the market prices options.
Are the prices of options accurately reflected by option models? Let's contrast the distribution of stock index
movements with the log-normal distribution postulated in most option models. We can attempt to understand the way prices actually move, and also why the market has a tendency to price options so that those struck farther from the market have implied volatilities that are higher, forming what is referred to as a smile pattern. I will present two examples of the smile pattern, one based on the implied volatilities of a group of equity options and the other applied to Intel [INTC] options. Understanding why this pattern exists can help option traders determine when they are considering a specific option trade.