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Numerical Methods and Optimization in Finance by Enrico Schumann, Dietmar Maringer, Manfred Gilli

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Chapter Seven

Modeling Dependencies

Publisher Summary

For many applications, one needs random variates that are dependent in a predetermined way. The first aim is to generate a matrix X of size N × p. The most-used measure of dependence is linear correlation. Assume two random variables Y and Z. Then for a sample of N paired observations (y1, z1), (y2, z2), . . . , (yN, zN) linear correlation ρ is computed. Markov chains is another model of dependence. This approach is particularly useful for time series with conditional probabilities, and Markov chain Monte Carlo plays a very prominent role in financial simulations. In its simplest version, there is only a limited set of alternatives, and the probabilities for the next state of a variable only ...

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