Abstract
The Backward Stochastic Differential Equation (BSDE) is an important tool for pricing and hedging. Highly accurate pricing for low computation time becomes interesting for minimizing monetary loss. Therefore, we explore the opportunity of parallelizing high-order multistep schemes in option pricing. In the multistep scheme the computations at each space grid point are independent and this fact motivates us to select massively parallel GPU computing using CUDA. In our investigations we identify performance bottlenecks and apply appropriate optimization techniques to reduce the computation time in a uniform space domain. Runtime experiments manifest optimistic speedups for the parallel implementation on a single GPU, NVIDIA GeForce 1070 Ti.
Highlights
The backward stochastic differential equations (BSDEs) have been widely used in various areas such as physics and finance due to one of their key features, namely they provide a probabilistic representation of solutions of nonlinear parabolic partial differential equations (PDEs)
Some acceleration strategies based on Graphics Processing Unit (GPU) computing have been developed for the pricing problems in finance, a very little of them are BSDE-based approach
In this work we investigate the massively parallel GPU computing in the multistep scheme [27], to make the scheme be more useful in practice
Summary
The backward stochastic differential equations (BSDEs) have been widely used in various areas such as physics and finance due to one of their key features, namely they provide a probabilistic representation of solutions of nonlinear parabolic partial differential equations (PDEs). Some acceleration strategies based on Graphics Processing Unit (GPU) computing have been developed for the pricing problems in finance, a very little of them are BSDE-based approach. These works can be found in [7, 11, 22], where the acceleration strategies are applied on numerical methods of convergence order not higher than 2. In [13], we have successfully parallelized that multistep scheme on GPUs, and showed the gain in computational time for option pricing via the Black-Scholes BSDE.
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