论文标题
张量的波动率校准
Tensoring volatility calibration
论文作者
论文摘要
近年来，灵感来自一系列引人注目的论文，这些论文使用深度神经网以实质上加快了定价模型的校准，我们研究了Chebyshev张量而不是深神经网的使用。鉴于在某些情况下，Chebyshev张量可以比深神经网更有效地探索要近似函数的输入空间，这是由于其指数收敛，因此定价模型的校准问题似乎是一个很好的情况，是Chebyshev Tensors可以表现出色的一个很好的情况。 在这项研究中，我们直接或借助张量扩展算法构建了Chebyshev张量，以应对与粗糙Bergomi波动性模型校准相关的计算瓶颈。结果令人鼓舞，因为通过Chebyshev张量的模型校准的准确性与使用深神经网时相似，但是在实验中，建筑工作的效率在5到100倍的范围内。我们的测试表明，当使用Chebyshev张量时，粗糙的Bergomi波动率模型的校准效率比通过Brute-Force校准（使用定价函数）高约40,000倍。
Inspired by a series of remarkable papers in recent years that use Deep Neural Nets to substantially speed up the calibration of pricing models, we investigate the use of Chebyshev Tensors instead of Deep Neural Nets. Given that Chebyshev Tensors can be, under certain circumstances, more efficient than Deep Neural Nets at exploring the input space of the function to be approximated, due to their exponential convergence, the problem of calibration of pricing models seems, a priori, a good case where Chebyshev Tensors can excel. In this piece of research, we built Chebyshev Tensors, either directly or with the help of the Tensor Extension Algorithms, to tackle the computational bottleneck associated with the calibration of the rough Bergomi volatility model. Results are encouraging as the accuracy of model calibration via Chebyshev Tensors is similar to that when using Deep Neural Nets, but with building efforts that range between 5 and 100 times more efficient in the experiments run. Our tests indicate that when using Chebyshev Tensors, the calibration of the rough Bergomi volatility model is around 40,000 times more efficient than if calibrated via brute-force (using the pricing function).
