Derivatives

Abstract

This chapter gives an introduction to the markets for derivative securities and illustrates how such derivatives can be priced using the general theory developed in earlier chapters and, in particular, the risk-adjusted probability measures from Ch. 12. First, forwards and futures are described and contrasted, and general expressions for forward and futures prices are derived. Next, options are considered. For European-style options general, but rather abstract, pricing formulas are derived, after which the specialization to a lognormal setting is shown to produce more directly applicable pricing formulas with the Black-Scholes formula as an important special case. Various pricing formulas for European options on bonds or interest rates are also obtained. The cash flows and valuation of interest rate swaps and options on such swaps are explained. Finally, the complications involved in pricing American-style options are discussed.