论文标题
Markovian近似蒙特卡洛的粗糙Bergomi模型定价
Markovian approximation of the rough Bergomi model for Monte Carlo option pricing
论文作者
论文摘要
最近开发的粗糙Bergomi（Rbergomi）模型是一种粗糙的分数随机波动率（RFSV）模型，它可以与其他RFSV模型相比，可以生成更现实的术语结构。然而，其非马克维亚性为模型校准和模拟带来了数学和计算挑战。为了克服这些困难，我们表明Rbergomi模型可以由具有马尔可维亚特性的Bergomi模型近似。我们的主要理论结果是建立和描述Rbergomi模型的仿射结构。我们通过基于混合方案实施马尔可夫近似算法来证明我们方法的效率和准确性。
The recently developed rough Bergomi (rBergomi) model is a rough fractional stochastic volatility (RFSV) model which can generate more realistic term structure of at-the-money volatility skews compared with other RFSV models. However, its non-Markovianity brings mathematical and computational challenges for model calibration and simulation. To overcome these difficulties, we show that the rBergomi model can be approximated by the Bergomi model, which has the Markovian property. Our main theoretical result is to establish and describe the affine structure of the rBergomi model. We demonstrate the efficiency and accuracy of our method by implementing a Markovian approximation algorithm based on a hybrid scheme.
