High Performance Computational Finance 

Abstract: It has been shown that the sparse grid combination technique can be a practical tool to solve high dimensional PDEs arising in multidimensional option pricing problems in finance. Hierarchical approximation of these problems leads to linear systems that are smaller in size compared to those arising from standard finite element or finite difference discretizations. However, these systems are still excessively demanding in terms of memory for direct methods and challenging to solve by iterative methods. In this paper we address iterative solutions via preconditioned Krylov subspace based methods, such as Stabilized BiConjugate Gradient (BiCGStab) and CG Squared (CGS), with the main focus on the design of such iterative solvers to harness massive parallelism of general purpose Graphics Processing Units (GPGPU)s. We discuss data structures and efficient implementation of iterative solvers. We also present a number of performance results to demonstrate the scalability of these solvers on the NVIDIA's CUDA platform.

Abstract: Deep neural networks (DNNs) are powerful types of artificial neural networks (ANNs) that use several hidden layers. They have recently gained considerable attention in the speech transcription and image recognition community (Krizhevsky et al., 2012) for their superior predictive properties including robustness to overfitting. However their application to financial market prediction has not been previously researched, partly because of their computational complexity. This paper describes the application of DNNs to predicting financial market movement directions. A critical step in the viability of the approach in practice is the ability to effectively deploy the algorithm on general purpose high performance computing infrastructure. Using an Intel Xeon Phi co-processor with 61 cores, we describe the process for efficient implementation of the batched stochastic gradient descent algorithm and demonstrate a 11.4x speedup on the Intel Xeon Phi over a serial implementation on the Intel Xeon.

Abstract: Computational finance relies heavily on the use of Monte Carlo simulation techniques. However, Monte Carlo simulation is computationally very demanding. We demonstrate the use of architecturally diverse systems to accelerate the performance of these simulations, exploiting both graphics processing units and field-programmable gate arrays. Performance results include a speedup of 74times relative to an 8 core multiprocessor system (180times relative to a single processor core).

Abstract: Huge growth in the trading and complexity of credit derivative instruments over the past five years has driven the need for ever more computationally demanding mathematical models. This has led to massive growth in data center compute capacity, power and cooling requirements. We report the results of an on-going joint project between J.P. Morgan and specialist acceleration solutions provider Maxeler Technologies to improve the price-performance for calculating the value and risk of a large complex credit derivatives portfolio. Our results show that valuing tranches of Collateralized Default Obligations (CDOs) on Maxeler accelerated systems is over 30 times faster per cubic foot and per Watt than solutions using standard multi-core Intel Xeon processors. We also report some preliminary results of further work that extends the approach to classes of interest rate derivatives.