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首页> 外文期刊>Computational economics >Unified Approach for the Affine and Non-affine Models: An Empirical Analysis on the S&P 500 Volatility Dynamics
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Unified Approach for the Affine and Non-affine Models: An Empirical Analysis on the S&P 500 Volatility Dynamics

机译：仿射模型和非仿射模型的统一方法：对S＆P 500波动率动力学的实证分析

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摘要

Being able to generate a volatility smile and adequately explain how it moves up and down in response to changes in risk, stochastic volatility models have replaced BS model. A single-factor volatility model can generate steep smiles or flat smiles at a given volatility level, but it cannot generate both for given parameters. In order to match the market implied volatility surface precisely, Grasselli introduced a 4/2 stochastic volatility model that includes the Heston model and the 3/2 model, performing as affine and non-affine model respectively. The present paper is intended to further investigate the 4/2 model, which falls into four parts. First, we apply Lewis's fundamental transform approach instead of Grasselli's method to deduce PDEs, which is intuitional and simple; Then, we use a result derived by Craddock and Lennox using Lie Symmetries theory for PDEs, and the results are more objective and reasonable; Finally, through adopting the data on S&P 500, we estimate the parameters of the 4/2 model; Furthermore, we investigate the 4/2 model along with the Heston model and the 3/2 model and compare their different performances. Our results illustrate that the 4/2 model outperforms the Heston and the 3/2 model for the fitting problem.
机译：能够产生波动性微笑并充分说明其如何响应风险变化而向上和向下移动，随机波动率模型已取代了BS模型。单因素波动率模型可以在给定的波动率水平下产生陡峭的笑容或平坦的笑容，但是对于给定的参数，它不能同时生成这两个函数。为了精确匹配市场隐含波动率表面，Grasselli引入了一个4/2随机波动率模型，其中包括Heston模型和3/2模型，分别用作仿射模型和非仿射模型。本文旨在进一步研究4/2模型，该模型分为四个部分。首先，我们用Lewis的基本变换方法代替Grasselli的方法来推导PDE，这是直观且简单的。然后，我们采用了由Craddock和Lennox运用李对称性理论推导的PDE的结果，该结果更加客观合理。最后，通过采用标准普尔500指数的数据，我们估算了4/2模型的参数。此外，我们研究了4/2模型以及Heston模型和3/2模型，并比较了它们的不同性能。我们的结果表明，对于拟合问题，4/2模型优于Heston和3/2模型。

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