Title :
Pricing multi-asset American options on Graphics Processing Units using a PDE approach
Author :
Dang, Duy Minh ; Christara, Christina C. ; Jackson, Kenneth R.
Author_Institution :
Department of Computer Science, University of Toronto, ON, M5S 3G4, Canada
Abstract :
We develop highly efficient parallel pricing methods on Graphics Processing Units (GPUs) for multi-asset American options via a Partial Differential Equation (PDE) approach. The linear complementarity problem arising due to the free boundary is handled by a penalty method. Finite difference methods on uniform grids are considered for the space discretization of the PDE, while classical finite differences, such as Crank-Nicolson, are used for the time discretization. The discrete nonlinear penalized equations at each timestep are solved using a penalty iteration. A GPU-based parallel Alternating Direction Implicit Approximate Factorization technique is employed for the solution of the linear algebraic system arising from each penalty iteration. We demonstrate the efficiency and accuracy of the parallel numerical methods by pricing American options written on three assets.
Keywords :
Approximation methods; Graphics processing unit; Instruction sets; Jacobian matrices; Kernel; Pricing; Tiles; Alternating Direction Implicit Approximate Factorization; American option; GPUs; Graphics Processing Units; finite difference; multi-asset; parallel computing; penalty method;
Conference_Titel :
High Performance Computational Finance (WHPCF), 2010 IEEE Workshop on
Conference_Location :
New Orleans, LA, USA
Print_ISBN :
978-1-4244-9062-2
DOI :
10.1109/WHPCF.2010.5671831