Option Valuation Models
17.1 CHAPTER OVERVIEW
Later chapters use the standard option pricing model originally developed by Black, Scholes, and Merton. They explore the practical applications of the model in pricing options and strategies, and its sensitivities as measured by the so-called ‘Greeks’: delta, gamma, theta, vega, and rho. The current chapter provides a more detailed insight into how options are priced, and may be skipped over by readers who are more concerned with applications. At the same time it is not intended to cover the more complex mathematics of option pricing. The chapter shows that an option pricing model has to meet certain constraints, and moves on to demonstrate a key result, the put-call parity relationship. A simple option valuation model is developed using a one-step and then a three-step binomial tree, with the volatility of the underlying incorporated into the model. As more and more steps are added to the tree the option value converges on that calculated by the famous Black-Scholes option pricing model. The Black-Scholes equation is presented in a manner that can easily be set up in a spreadsheet. Finally, the chapter looks at some of the simplifying assumptions made by the model, the circumstances in which they tend to break down, and how option traders compensate for these problems in practice. The Appendix shows how to calculate the volatility of an asset based on its historical returns.
17.2 FUNDAMENTAL PRINCIPLES: EUROPEAN OPTIONS