论文标题
关于仿射扩散过程的随机化，并应用于VIX和S＆P 500的选项定价
On Randomization of Affine Diffusion Processes with Application to Pricing of Options on VIX and S&P 500
论文作者
论文摘要
由于其封闭形式的特征功能（CHF），仿射（跳跃）扩散类（AD）在从业者和研究人员中获得了极大的普及。但是，有明确的证据表明，线性约束不足以进行精确且一致的选项定价。任何非携带模型都必须通过快速校准的严格要求 - 这通常具有挑战性。我们在这里专注于随机AD（RAND）模型，即，我们允许模型参数的外源随机性。定价模型的随机化发生在仿射模型之外，因此形成了放宽亲和力约束的概括。该方法是通用的，可以应用于任何模型参数。它依赖于所谓的随机器的矩存在 - 随机参数的随机变量。 RAND模型允许灵活性，同时受益于快速校准和建立良好的大型蒙特卡洛模拟，通常可用于广告流程。本文将讨论RAND方法的理论和实际方面，例如相应CHF的推导，仿真和敏感性计算。我们还将说明在标准普尔500和VIX上始终如一的选项定价中，随机随机波动率模型的优势。
The class of Affine (Jump) Diffusion (AD) has, due to its closed form characteristic function (ChF), gained tremendous popularity among practitioners and researchers. However, there is clear evidence that a linearity constraint is insufficient for precise and consistent option pricing. Any non-affine model must pass the strict requirement of quick calibration -- which is often challenging. We focus here on Randomized AD (RAnD) models, i.e., we allow for exogenous stochasticity of the model parameters. Randomization of a pricing model occurs outside the affine model and, therefore, forms a generalization that relaxes the affinity constraints. The method is generic and can apply to any model parameter. It relies on the existence of moments of the so-called randomizer- a random variable for the stochastic parameter. The RAnD model allows flexibility while benefiting from fast calibration and well-established, large-step Monte Carlo simulation, often available for AD processes. The article will discuss theoretical and practical aspects of the RAnD method, like derivations of the corresponding ChF, simulation, and computations of sensitivities. We will also illustrate the advantages of the randomized stochastic volatility models in the consistent pricing of options on the S&P 500 and VIX.
