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

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Chapter 12

Discrete time approximations

In this chapter we introduce some basic issues concerning discrete time approximations of stochastic differential equations, which are used in a later chapter to estimate the parameters in SDEs using the Generalized Method of Moments (GMM). Furthermore the methods are used to simulate discrete observations from a continuous time system, which, for example, can be used to determine the price of a financial derivative in cases where no closed form solution of the pricing formula exist.

12.1 Stochastic Taylor expansion

The stochastic Taylor expansion is a stochastic counterpart of the Taylor expansion in a deterministic framework, and it is essential for the discrete time approximation of stochastic differential ...

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