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

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Chapter 9

Continuous-time security markets

In this chapter we consider financial markets in continuous time, contrary to the discrete time approach in Chapter 3. The multiperiod binomial model considered in Chapter 3 allowed the asset prices to take only one of two values in the next period, which certainly contradicts the actual behaviour of stock prices. In real financial markets, trading is not restricted only to take place at a limited number of time points; hence, it seems reasonable to model the financial market in continuous time where the prices are allowed to change at any time.1 The mathematical description of a stochastic process in continuous time presented in Chapter 8 will be used to model the price of securities.

9.1 From discrete ...

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