Seminar series
Date
Fri, 04 Feb 2011
14:15
Location
DH 1st floor SR
Speaker
Dr Anke Wiese
Organisation
Heriot-Watt University

In the Heston stochastic volatility model, the variance process is given by a mean-reverting square-root process. It is known that its transition probability density can be represented by a non-central chi-square density. There are fundamental differences in the behaviour of the variance process depending on the number of degrees of freedom: if the number of degrees of freedom is larger or equal to 2, the zero boundary is unattainable; if it is smaller than 2, the zero boundary is attracting and attainable.

We focus on the attainable zero boundary case and in particular the case when the number of degrees of freedom is smaller than 1, typical in foreign exchange markets. We prove a new representation for the density based on powers of generalized Gaussian random variables. Further we prove that Marsaglia's polar method extends to the generalized Gaussian distribution, providing an exact and efficient method for generalized Gaussian sampling. Thus, we establish a new exact and efficient method for simulating the Cox-Ingersoll-Ross process for an attracting and attainable zero boundary, and thus establish a new simple method for simulating the Heston model.

We demonstrate our method in the computation of option prices for parameter cases that are described in the literature as challenging and practically relevant.

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