OVERVIEW

This chapter discusses some of the various kinds of options and how they are used. It presents the Black-Scholes options pricing model and discusses its assumptions and its key features. It also presents a slightly different mathematical approach for development of the standard compound interest functions. It presents several problems with using Black-Scholes for bond option pricing, and it mentions fractal analysis as an alternative conceptual framework for option evaluation.

The Black-Scholes options pricing model is related to, and can be derived from, the partial differential equation for heat diffusion, first published by the French mathematician Fourier in the early 19th century. Development of this equation, and similar related mathematical work in options, is far beyond the scope of this book and requires mathematical skills and knowledge not assumed by this book. These include a good knowledge of probability, continuous probability distribution functions (especially the normal, or Gaussian, distribution), mathematical statistics, and partial differential equations. However, we can give the reader some idea of what is going on with this equation.

Managers, investment supervisors, and many investors may need only to have a general knowledge of the subject to work successfully in the field. Others will want to learn much more. The field of options is enormous and complicated. Those without much background in mathematics might look at the McMillan book and possibly the Mandelbrot article, listed in the suggestions for further reading at end of this chapter. Others may wish to study the mathematics of options further or...