Chapter 7 A discrete time synthesis of derivative security valuation using a term structure of futures prices

Abstract

Summary This paper provided an analytic synthesis of the option pricing literature, using a term structure of futures prices approach. Postulating a process for the evolution of the term structure of futures prices, it is shown how to price derivative secutities in an arbitrage-free manner. Complete markets are assumed. This approach generalizes the traditional methodology by relaxing the assumption of a frictionless spot market (or even the existence of a spot market) and that the underlying commodity is storable. Thus, this method is consistent with short sale constraints in the spot market for the underlying commodity. When short sale restrictions are removed, the traditional option pricing models are shown to be obtainable as special cases. This includes the binomial model of CRR, as well as its applications to index options, currency options and commodity options. The new interest rate options models of HJM are also shown to be a subset of this framework. A brief discussion of how to empirically implement the model is also provided. References are given to reviews of the empirical literature and historic surveys of the model development.