论文标题
Quintic Ornstein-uhlenbeck波动率模型，该模型共同校准SPX＆VIX Smiles
The quintic Ornstein-Uhlenbeck volatility model that jointly calibrates SPX & VIX smiles
论文作者
论文摘要
Quintic Ornstein-uhlenbeck波动率模型是一个随机波动率模型，其中波动率过程是单个Ornstein-Uhlenbeck过程的多项式函数，具有快速平均值和大量VOL。该模型能够获得SPX-VIX微笑的显着关节，只有6个有效参数和一个允许匹配某些项结构的输入曲线。我们提供了输入曲线的几种实际规格，研究它们对关节校准问题的影响，并考虑额外的时间依赖性参数，以帮助获得更好的拟合，以使更长的成熟度超过1年。更好的是，该模型对于定价和校准仍然非常简单且可进行：在Ornstein-uhlenbeck过程中，VIX平方再次是多项式，从而导致通过对高斯密度的简单整合而导致有效的VIX导数定价；精确的波动过程模拟；定价SPX产品衍生物可以通过具有合适的对立和控制变体的标准蒙特卡洛技术有效，准确地完成。
The quintic Ornstein-Uhlenbeck volatility model is a stochastic volatility model where the volatility process is a polynomial function of degree five of a single Ornstein-Uhlenbeck process with fast mean reversion and large vol-of-vol. The model is able to achieve remarkable joint fits of the SPX-VIX smiles with only 6 effective parameters and an input curve that allows to match certain term structures. We provide several practical specifications of the input curve, study their impact on the joint calibration problem and consider additionally time-dependent parameters to help achieve better fits for longer maturities going beyond 1 year. Even better, the model remains very simple and tractable for pricing and calibration: the VIX squared is again polynomial in the Ornstein-Uhlenbeck process, leading to efficient VIX derivative pricing by a simple integration against a Gaussian density; simulation of the volatility process is exact; and pricing SPX products derivatives can be done efficiently and accurately by standard Monte Carlo techniques with suitable antithetic and control variates.
