论文标题
RBergomi模型中的VIX定价在制度转换措施变化下
VIX pricing in the rBergomi model under a regime switching change of measure
论文作者
论文摘要
物理度量下的Rbergomi模型包括将对数变化的建模为截断的布朗人半固定过程。然后，应用了措施的确定性更改。 Rbergomi模型能够以很少的参数复制观察到的市场SP500微笑，但由于测量的确定性变化，与在市场上观察到的向上倾斜的微笑相比，会产生平坦的Vix笑容。我们使用精确的解决方案进行某些不均匀的分数Ornstein-uhlenbeck方程来构建RBERGOMI模型的量度变化的制度转换，该模型都可以在向上倾斜的VIX微笑，并且配备了有效的半分析Monte Carlo方法，可以将其用于价格VIX的价格VIX。该模型还允许近似VIX，从而大大降低了定价VIX选项和期货的计算成本。基于基本连续时间马尔可夫链的差异技术使我们能够进一步降低计算成本。我们通过对模型进行校准以观察到市场微笑并讨论结果来验证我们的模型的功能。
The rBergomi model under the physical measure consists of modeling the log-variance as a truncated Brownian semi-stationary process. Then, a deterministic change of measure is applied. The rBergomi model is able to reproduce observed market SP500 smiles with few parameters, but by virtue of the deterministic change of measure, produces flat VIX smiles, in contrast to the upward sloping smiles observed in the market. We use the exact solution for a certain inhomogeneous fractional Ornstein-Uhlenbeck equation to build a regime switching stochastic change of measure for the rBergomi model that both yields upward slopping VIX smiles and is equipped with an efficient semi-analytic Monte Carlo method to price VIX options. The model also allows an approximation of the VIX, which leads to a significant reduction of the computational cost of pricing VIX options and futures. A variance reduction technique based on the underlying continuous time Markov chain allows us to further reduce the computational cost. We verify the capabilities of our model by calibrating it to observed market smiles and discuss the results.
