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A Course in Financial Calculus by Alison Etheridge

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1 Single period models

Summary

In this chapter we introduce some basic definitions from finance and investigate the problem of pricing financial instruments in the context of a very crude model. We suppose the market to be observed at just two times: zero, when we enter into a financial contract; and T, the time at which the contract expires. We further suppose that the market can only be in one of a finite number of states at time T. Although simplistic, this model reveals the importance of the central paradigm of modern finance: the idea of a perfect hedge. It is also adequate for a preliminary discussion of the notion of ‘complete market’ and its importance if we are to find a ‘fair’ price for our financial contract.

The proofs in §1.5 can ...

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