论文标题
具有基于分析梯度的随机波动率的Libor市场模型快速校准
Fast calibration of the LIBOR Market Model with Stochastic Volatility based on analytical gradient
论文作者
论文摘要
我们提议利用以随机波动率和流离失所的扩散（DDSVLMM）在Libor市场模型中建模的掉期速率过程的特征功能的常识，以得出有关模型参数的交换价格梯度价格的分析表达。我们使用此结果来使用基于梯度的优化算法为DDSVLMM得出有效的校准方法。我们的研究依赖并扩展了（Cui等，2017）的工作，该工作开发了基于Heston Moment生成函数的替代表述（del Ba {del ba { ^q。我们的主要结论是，基于分析梯度的校准对DDSVLMM具有很高的竞争力，因为它显着限制了优化算法中的步骤数，同时提高了其准确性。将这种新方法的效率与经典的标准优化程序进行了比较。
We propose to take advantage of the common knowledge of the characteristic function of the swap rate process as modelled in the LIBOR Market Model with Stochastic Volatility and Displaced Diffusion (DDSVLMM) to derive analytical expressions of the gradient of swaptions prices with respect to the model parameters. We use this result to derive an efficient calibration method for the DDSVLMM using gradient-based optimization algorithms. Our study relies on and extends the work by (Cui et al., 2017) that developed the analytical gradient for fast calibration of the Heston model, based on an alternative formulation of the Heston moment generating function proposed by (del Ba{ñ}o et al., 2010). Our main conclusion is that the analytical gradient-based calibration is highly competitive for the DDSVLMM, as it significantly limits the number of steps in the optimization algorithm while improving its accuracy. The efficiency of this novel approach is compared to classical standard optimization procedures.
