论文标题
在控制隐含波动时的短速率模型，分析定价和灵活性的随机化
Randomization of Short-Rate Models, Analytic Pricing and Flexibility in Controlling Implied Volatilities
论文作者
论文摘要
我们专注于扩展现有的短速率模型，从而在保留分析性的同时控制生成的隐含波动率。我们通过将随机仿射扩散（RAND）方法应用于Heath-Jarrow-Morton框架下的短期过程类别来实现这一目标。在无套度条件下，模型参数可以是外源随机的，从而促进了增强校准程序的其他自由度。我们表明，对于随机的短速率模型，即使对于标准的1D变体，也可以控制隐含波动率的形状，并显着提高模型校准的质量。特别是，我们说明应用于船体白色模型的随机化导致局部波动率类型的动态，并明确可用标准波动率敏感的衍生物的价格。随机的船体白（RHW）模型提供了几乎完美的校准，适合暗示的划分。
We focus on extending existing short-rate models, enabling control of the generated implied volatility while preserving analyticity. We achieve this goal by applying the Randomized Affine Diffusion (RAnD) method to the class of short-rate processes under the Heath-Jarrow-Morton framework. Under arbitrage-free conditions, the model parameters can be exogenously stochastic, thus facilitating additional degrees of freedom that enhance the calibration procedure. We show that with the randomized short-rate models, the shapes of implied volatility can be controlled and significantly improve the quality of the model calibration, even for standard 1D variants. In particular, we illustrate that randomization applied to the Hull-White model leads to dynamics of the local volatility type, with the prices for standard volatility-sensitive derivatives explicitly available. The randomized Hull-White (rHW) model offers an almost perfect calibration fit to the swaption implied volatilities.
