Chapter 3

Discrete Time and State Models

The chapter briefly reviews basic financial concepts, including present value, annuities, and growth models. The main subject of the text, no-arbitrage pricing, is introduced to price a finite system of bonds in discrete finite time. After presenting models of certainty over finite numbers of time periods, the chapter presents models of uncertainty over a single period. The first probabilistic model is developed to price a finite number of securities using Arrow–Debreu (pure) securities. After introducing uncertainty in single period models, multiperiod models under uncertainty are introduced. Concepts of synthetic and risk-neutral probabilities and their importance in arbitrage-free pricing are contrasted ...

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