Monte Carlo sampling given a Characteristic Function: Quantile Mechanics in Momentum Space
AbstractIn mathematical finance and other applications of stochastic processes, it is frequently the case that the characteristic function may be known but explicit forms for density functions are not available. The simulation of any distribution is greatly facilitated by a knowledge of the quantile function, by which uniformly distributed samples may be converted to samples of the given distribution. This article analyzes the calculation of a quantile function direct from the characteristic function of a probability distribution, without explicit knowledge of the density. We form a non-linear integro-differential equation that despite its complexity admits an iterative solution for the power series of the quantile about the median. We give some examples including tail models and show how to generate C-code for examples.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 0903.1592.
Date of creation: Mar 2009
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-09-26 (All new papers)
- NEP-ECM-2009-09-26 (Econometrics)
- NEP-ORE-2009-09-26 (Operations Research)
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