Positive and implicit stochastic volatility simulation
Positive and implicit stochastic volatility simulation
复制标题
DOI：
--
复制
发表时间：
2008-02
期刊：
影响因子：
--
通讯作者：
William G. Halley;S. Malham;Anke Wiese
中科院分区：
文献类型：
--
作者：
William G. Halley;S. Malham;Anke Wiese
对于非线性随机微分系统，在零边界非吸引的情况下，我们发展了强全隐式保正数值方法。这些方法都是隐式的扩散矢量场。因此，他们适用于一个限制类，即那些次线性形式。然而，这仍然包括大多数朗之万衍生过程的波动模型在金融和物理学分子模拟的典型。当零边界是吸引和可达到的，我们专注于一个原型模型，即均值回复Cox-Ingersoll-Ross过程。因此，我们考虑非中心卡方跃迁密度与分数自由度。我们证明了我们可以从这个密度通过模拟泊松分布的广义高斯随机变量的幂和的抽样。进一步证明了Marsaglia的极坐标方法推广到广义高斯分布，为广义高斯抽样提供了一种精确有效的方法。我们应用我们的方法，方差曲线模型和赫斯顿模型。
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.