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Statistics for Finance by Erik Lindström, Henrik Madsen, Jan Nygaard Nielsen

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Chapter 3

Discrete time finance

This chapter will describe discrete time models in order to introduce the reader to some of the basic concepts to be used in subsequent chapters on continuous time. The theory in discrete time is simpler as the proofs only require linear algebra.

In this chapter we shall consider simple models of security markets and describe the basic principles of valuation of contingent claims (e.g., options, futures). The key idea behind valuation in markets with uncertainty is the notion of absence of arbitrage. Roughly speaking, an arbitrage is a situation where an investor, through buying and selling securities, takes a “position” in the market which has zero net cost and which guarantees 1) no losses in the future and 2) ...

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