ABSTRACT
This chapter discusses multinomial generalization of the one-period binomial market model. Although single-period models cannot give a realistic representation of a complex, dynamically changing stock market, one uses such models to illustrate many important economic principles. The simplest example of financial contracts is Arrow—Debreu securities. To describe a portfolio in the model, the number of units held in the portfolio needs to be calculated for every base asset. There exist two types of arbitrage opportunities. One type of arbitrage is an investment that gives a positive reward at time 0 and has no future cost at a time T. Another type of arbitrage is an investment with zero initial value and nonnegative future cost that has a positive probability of yielding a strictly positive payoff at time T. The simplest single-period incomplete market model is a model with three states of the world.
