粗糙Bergomi模型的涡轮增压蒙特卡罗定价
Turbocharging Monte Carlo pricing for the rough Bergomi model
摘要：
Bayer、Friz和Gatheral提出的粗糙Bergomi模型[Quant. Finance 16（6），887-904，2016]，是最近的粗略波动率模型之一，与隐含波动率表面基本上是时不变的程式化事实一致，并且能够捕捉在股票市场中观察到的偏斜的期限结构。在没有分析的欧式期权定价方法的模型，我们专注于减少运行时调整方差的蒙特卡罗隐含波动率，从而有助于模型的模拟校准。我们采用了一种新的组合方差缩减方法，立即适用于任何条件对数正态随机波动率模型。假设一个目标隐含波动率估计与给定程度的信心，因此校准RMSE，我们证明的结果相当于显着的运行时间减少-大约20倍，平均在不同的相关性制度。
英文摘要：
The rough Bergomi model, introduced by Bayer, Friz and Gatheral [Quant. Finance 16(6), 887-904, 2016], is one of the recent rough volatility models that are consistent with the stylised fact of implied volatility surfaces being essentially time-invariant, and are able to capture the term structure of skew observed in equity markets. In the absence of analytical European option pricing methods for the model, we focus on reducing the runtime-adjusted variance of Monte Carlo implied volatilities, thereby contributing to the model's calibration by simulation. We employ a novel composition of variance reduction methods, immediately applicable to any conditionally log-normal stochastic volatility model. Assuming one targets implied volatility estimates with a given degree of confidence, thus calibration RMSE, the results we demonstrate equate to significant runtime reductions - roughly 20 times on average, across different correlation regimes.
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