论文标题
希尔伯特太空值随机波动率模型的鲁棒性
Robustness of Hilbert space-valued stochastic volatility models
论文作者
论文摘要
在本文中，我们表明，由于测量或近似误差，希尔伯特空间价值随机模型在扰动方面是强大的，在潜在的波动过程中。在随机波动性调制的Ornstein-uhlenbeck过程中，我们量化了波动率在挥发性过程中的扰动而引起的误差。此外，当考虑驾驶复合泊松过程和半群发生器的有限尺寸近似方面，我们研究了波动率过程本身的鲁棒性，在考虑了值得验证的barndorff-nielsen和Shephard随机波动率模型时。我们还为平方根近似值提供结果。在所有情况下，我们都根据基础参数的近似值为诱导的误差提供明确的界限。我们讨论了一些适用于远期和波动性期权价格的稳健性。
In this paper we show that Hilbert space-valued stochastic models are robust with respect to perturbation, due to measurement or approximation errors, in the underlying volatility process. Within the class of stochastic volatility modulated Ornstein-Uhlenbeck processes, we quantify the error induced by the volatility in terms of perturbations in the parameters of the volatility process. We moreover study the robustness of the volatility process itself with respect to finite dimensional approximations of the driving compound Poisson process and semigroup generator respectively, when considering operator-valued Barndorff-Nielsen and Shephard stochastic volatility models. We also give results on square root approximations. In all cases we provide explicit bounds for the induced error in terms of the approximation of the underlying parameter. We discuss some applications to robustness of prices of options on forwards and volatility.
