Risk Finance and Asset Pricing: Value, Measurements, and Markets

CHAPTER 8

Options Applied

OVERVIEW

This chapter focuses on applications of the Arrow-Debreu theory, highlighting its many uses. A large variety of problems are treated including trading, immunization of portfolios, and short-selling as well as problems of pricing options, assets, and financial contracts. In addition, insurance contracts, infrastructure investments, pricing loans, and other problems are treated. The number of potential applications is extremely large and expanding in response to both needs and opportunities by and for investors and speculators. The chapter also provides an extension of the discrete state models considered in the previous chapter to the Black-Scholes continuous time lognormal model. Extensions to other models are profusely published and may be found in many standard financial engineering books as well as at the web site www.charlestapiero.com (where some of the problems outlined in this book are expanded). In addition, this chapter provides an introduction to the Greeks and their applications.

OPTION APPLICATIONS

To price assets we use essentially two techniques. One is based on replicating an asset to be priced by a portfolio whose price can be ascertained. Assuming that markets are complete, the law of the single price applies and therefore the asset and its replicating portfolio have necessarily the same price. In this sense, the price is only a construct indicative of the wants of buyers and sellers and the existence of an equilibrium based ...