Tensoring volatility calibration

TL;DR

This paper explores using Chebyshev Tensors as an efficient alternative to Deep Neural Nets for calibrating the rough Bergomi volatility model, achieving similar accuracy with significantly reduced computational effort.

Contribution

The study demonstrates that Chebyshev Tensors can substantially improve calibration efficiency over neural networks in financial models.

Findings

Chebyshev Tensors achieve similar calibration accuracy as neural networks.

Calibration with Chebyshev Tensors is 5 to 100 times more efficient to build.

Overall calibration process is around 40,000 times faster than brute-force methods.

Abstract

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).