CHI-SQUARE SIMULATION OF THE CIR PROCESS AND THE HESTON MODEL

Simon J. A. Malham () and Anke Wiese ()
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Simon J. A. Malham: Maxwell Institute for Mathematical Sciences and School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
Anke Wiese: Maxwell Institute for Mathematical Sciences and School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK

International Journal of Theoretical and Applied Finance (IJTAF), 2013, vol. 16, issue 03, 1-38

Abstract: The transition probability of a Cox–Ingersoll–Ross process can be represented by a non-central chi-square density. First, we establish a new representation for the central chi-square density based on sums of powers of generalized Gaussian random variables. Second, we show that Marsaglia's polar method extends to this distribution, providing a simple, exact, robust and efficient acceptance–rejection method for generalized Gaussian sampling and thus central chi-square sampling. Third, we derive a simple, high-accuracy, robust and efficient direct inversion method for generalized Gaussian sampling based on the Beasley–Springer–Moro method. Indeed the accuracy of the approximation to the inverse cumulative distribution function is to the tenth decimal place. We then apply our methods to non-central chi-square variance sampling in the Heston model. We focus on the case when the number of degrees of freedom is small and the zero boundary is attracting and attainable, typical in foreign exchange markets. Using the additivity property of the chi-square distribution, our methods apply in all parameter regimes.

Keywords: Generalized Gaussian; generalized Marsaglia method; direct inversion; chi-square sampling; CIR process; stochastic volatility (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (5)

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DOI: 10.1142/S0219024913500143

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