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Calibration of financial models based on Automatic Differentiation and High-Performance Computing
[Thesis]. Manchester, UK: The University of Manchester; 2018.
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Abstract
Stochastic models are commonly used in quantitative finance to describe the dynamics of the derivatives market. As the market quotes are constantly changing, the models need to be calibrated to make real-time investment decisions. This can involve the sensitivity calculation to support the calibration process and investment portfolio management. For investment portfolios consisting of thousands of assets and options, the sensitivity calculation and calibration process are computationally expensive. This thesis presents a number of approaches to sensitivity calculation and model calibration utilizing high-performance computing architectures and Automatic Differentiation that improve performance and accuracy in financial modeling when compared to finite differences and pathwise methods. A parallel Monte-Carlo engine has been developed using the Adjoint methods for the first-order sensitivity calculation and model calibration This addresses the sensitivity and calibration problem for general stochastic differential models. The engine supports multi-/many-core CPU, GPU and distributed computing architectures. The work utilizes a graph representation and overloading operators to express general stochastic differential models. The sensitivities for the model calibration are calculated in parallel via a single simulation by the Adjoint method with the gradient computation cost being 1.8x that of function evaluation. The computational experiments consider both the Heston model and Heston with term-structure. These show that the engine improves performance by up to two orders of magnitude when compared to a sequential version. A hardware implementation has been developed for the Heston model calibration via the Adjoint on FPGA. The work also shows performance improvement of up to two orders of magnitude when compared to a sequential implementation. A parallel non-linear least squares optimization framework using Automatic Differentiation has been developed. This utilizes a graph representation and overloaded operator techniques to express the general objective and constraint functions. The framework supports multi-/many-core architectures such as GPUs and Intel Xeon/Xeon-Phi. The computational experiments consider the semi-closed form Heston model with the Gauss-Kronrod integration. These show performance improvement of 8.4x on GPU (OpenCL) and 7x on (CUDA) vs a sequential OMP (OpenMP) implementation. A Xeon-Phi implementation improves performance by 34x when compared to a single-thread implementation.