Implied Volatility for European Options

Abstract

Black-Scholes theory, its explicit formulas presented in Chapter 3, or derived numerical methods for more complicated models to be discussed in the last part of this chapter and the next yield theoretical fair prices for various stock options. On the other hand, the real market prices of stock options, like market prices of anything else, are as high as someone is willing to pay for them, and as low as someone is willing to sell them for. It is a daily routine in options trading practice to reconcile theoretical and observed prices. It was also a matter of recent mathematical research to find new and better, more precise and more efficient methods for such a reconciliation. There are many mathematical methods of various degrees of sophistication to this end. The general rule is that the more precise the methods, the more demanding they are computationally as well.