Positive and implicit stochastic volatility simulation Export

@article{Halley2008, abstract = {For nonlinear stochastic differential systems, we develop strong fully implicit positivity preserving numerical methods in the case that the zero boundary is non-attracting. These methods are implicit in the diffusion vector fields. They thus apply to a restricted class, namely those with sublinear form. This however, still includes most Langevin derived processes typical of volatility models in finance and molecular simulation in physics. When the zero boundary is attracting and attainable, we specialize to a prototypical model, namely the mean-reverting Cox--Ingersoll--Ross process. We thus consider the non-central chi-squared transition density with fractional degrees of freedom. We prove that we can sample from this density by simulating Poisson distributed sums of 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. We apply our methods to a variance curve model and the Heston model.}, archivePrefix = {arXiv}, author = {{Halley}, W. and {Malham}, S. J. A. and {Wiese}, A.}, citeulike-article-id = {5088200}, citeulike-linkout-0 = {http://arxiv.org/abs/0802.4411}, citeulike-linkout-1 = {http://arxiv.org/pdf/0802.4411}, citeulike-linkout-2 = {http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2008arXiv0802.4411H}, day = {13}, eprint = {0802.4411}, journal = {ArXiv e-prints}, keywords = {for, multidimensional, positivity, preserving, schemes, sdes, solving, while}, month = {February}, posted-at = {2009-07-07 17:52:50}, priority = {2}, title = {Positive and implicit stochastic volatility simulation}, url = {http://arxiv.org/abs/0802.4411}, year = {2008} }

TY - JOUR ID - Halley2008 L3 - citeulike-article-id:5088200 N2 - For nonlinear stochastic differential systems, we develop strong fully implicit positivity preserving numerical methods in the case that the zero boundary is non-attracting. These methods are implicit in the diffusion vector fields. They thus apply to a restricted class, namely those with sublinear form. This however, still includes most Langevin derived processes typical of volatility models in finance and molecular simulation in physics. When the zero boundary is attracting and attainable, we specialize to a prototypical model, namely the mean-reverting Cox--Ingersoll--Ross process. We thus consider the non-central chi-squared transition density with fractional degrees of freedom. We prove that we can sample from this density by simulating Poisson distributed sums of 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. We apply our methods to a variance curve model and the Heston model. JF - ArXiv e-prints TI - Positive and implicit stochastic volatility simulation KW - for KW - multidimensional KW - positivity KW - preserving KW - schemes KW - sdes KW - solving KW - while AU - {Halley}, W AU - {Malham}, SJA AU - {Wiese}, A PY - 2008/February/13/ UR - http://arxiv.org/abs/0802.4411 ER -