  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).
