Modeling Multi-factor Financial Derivatives by a Partial Differential Equation Approach with Efficient Implementation on Graphics Processing Units

This thesis develops efficient modeling frameworks via a Partial Differential Equation (PDE) approach for multi-factor financial derivatives, with emphasis on three-factor models, and studies highly efficient implementations of the numerical methods on novel high-performance computer architectures,...

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Main Author: Dang, Duy Minh
Other Authors: Christara, Christina
Language:en_ca
Published: 2012
Subjects:
PDE
ADI
GPU
Online Access:http://hdl.handle.net/1807/42485
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spelling ndltd-LACETR-oai-collectionscanada.gc.ca-OTU.1807-424852014-01-03T03:43:33ZModeling Multi-factor Financial Derivatives by a Partial Differential Equation Approach with Efficient Implementation on Graphics Processing UnitsDang, Duy Minhmulti-currency swapsmulti-currency optionsPower Reverse-Dual CurrencyPRDCPartial Differential EquationPDEAlternating Direction ImplicitADIGraphics Processing UnitsGPUparallel computingfinite difference0984This thesis develops efficient modeling frameworks via a Partial Differential Equation (PDE) approach for multi-factor financial derivatives, with emphasis on three-factor models, and studies highly efficient implementations of the numerical methods on novel high-performance computer architectures, with particular focus on Graphics Processing Units (GPUs) and multi-GPU platforms/clusters of GPUs. Two important classes of multi-factor financial instruments are considered: cross-currency/foreign exchange (FX) interest rate derivatives and multi-asset options. For cross-currency interest rate derivatives, the focus of the thesis is on Power Reverse Dual Currency (PRDC) swaps with three of the most popular exotic features, namely Bermudan cancelability, knockout, and FX Target Redemption. The modeling of PRDC swaps using one-factor Gaussian models for the domestic and foreign interest short rates, and a one-factor skew model for the spot FX rate results in a time-dependent parabolic PDE in three space dimensions. Our proposed PDE pricing framework is based on partitioning the pricing problem into several independent pricing subproblems over each time period of the swap's tenor structure, with possible communication at the end of the time period. Each of these subproblems requires a solution of the model PDE. We then develop a highly efficient GPU-based parallelization of the Alternating Direction Implicit (ADI) timestepping methods for solving the model PDE. To further handle the substantially increased computational requirements due to the exotic features, we extend the pricing procedures to multi-GPU platforms/clusters of GPUs to solve each of these independent subproblems on a separate GPU. Numerical results indicate that the proposed GPU-based parallel numerical methods are highly efficient and provide significant increase in performance over CPU-based methods when pricing PRDC swaps. An analysis of the impact of the FX volatility skew on the price of PRDC swaps is provided. In the second part of the thesis, we develop efficient pricing algorithms for multi-asset options under the Black-Scholes-Merton framework, with strong emphasis on multi-asset American options. Our proposed pricing approach is built upon a combination of (i) a discrete penalty approach for the linear complementarity problem arising due to the free boundary and (ii) a GPU-based parallel ADI Approximate Factorization technique for the solution of the linear algebraic system arising from each penalty iteration. A timestep size selector implemented efficiently on GPUs is used to further increase the efficiency of the methods. We demonstrate the efficiency and accuracy of the proposed GPU-based parallel numerical methods by pricing American options written on three assets.Christara, ChristinaJackson, Kenneth2012-032013-11-15T22:08:42ZWITHHELD_ONE_YEAR2013-11-15T22:08:42Z2013-11-15Thesishttp://hdl.handle.net/1807/42485en_ca
collection NDLTD
language en_ca
sources NDLTD
topic multi-currency swaps
multi-currency options
Power Reverse-Dual Currency
PRDC
Partial Differential Equation
PDE
Alternating Direction Implicit
ADI
Graphics Processing Units
GPU
parallel computing
finite difference
0984
spellingShingle multi-currency swaps
multi-currency options
Power Reverse-Dual Currency
PRDC
Partial Differential Equation
PDE
Alternating Direction Implicit
ADI
Graphics Processing Units
GPU
parallel computing
finite difference
0984
Dang, Duy Minh
Modeling Multi-factor Financial Derivatives by a Partial Differential Equation Approach with Efficient Implementation on Graphics Processing Units
description This thesis develops efficient modeling frameworks via a Partial Differential Equation (PDE) approach for multi-factor financial derivatives, with emphasis on three-factor models, and studies highly efficient implementations of the numerical methods on novel high-performance computer architectures, with particular focus on Graphics Processing Units (GPUs) and multi-GPU platforms/clusters of GPUs. Two important classes of multi-factor financial instruments are considered: cross-currency/foreign exchange (FX) interest rate derivatives and multi-asset options. For cross-currency interest rate derivatives, the focus of the thesis is on Power Reverse Dual Currency (PRDC) swaps with three of the most popular exotic features, namely Bermudan cancelability, knockout, and FX Target Redemption. The modeling of PRDC swaps using one-factor Gaussian models for the domestic and foreign interest short rates, and a one-factor skew model for the spot FX rate results in a time-dependent parabolic PDE in three space dimensions. Our proposed PDE pricing framework is based on partitioning the pricing problem into several independent pricing subproblems over each time period of the swap's tenor structure, with possible communication at the end of the time period. Each of these subproblems requires a solution of the model PDE. We then develop a highly efficient GPU-based parallelization of the Alternating Direction Implicit (ADI) timestepping methods for solving the model PDE. To further handle the substantially increased computational requirements due to the exotic features, we extend the pricing procedures to multi-GPU platforms/clusters of GPUs to solve each of these independent subproblems on a separate GPU. Numerical results indicate that the proposed GPU-based parallel numerical methods are highly efficient and provide significant increase in performance over CPU-based methods when pricing PRDC swaps. An analysis of the impact of the FX volatility skew on the price of PRDC swaps is provided. In the second part of the thesis, we develop efficient pricing algorithms for multi-asset options under the Black-Scholes-Merton framework, with strong emphasis on multi-asset American options. Our proposed pricing approach is built upon a combination of (i) a discrete penalty approach for the linear complementarity problem arising due to the free boundary and (ii) a GPU-based parallel ADI Approximate Factorization technique for the solution of the linear algebraic system arising from each penalty iteration. A timestep size selector implemented efficiently on GPUs is used to further increase the efficiency of the methods. We demonstrate the efficiency and accuracy of the proposed GPU-based parallel numerical methods by pricing American options written on three assets.
author2 Christara, Christina
author_facet Christara, Christina
Dang, Duy Minh
author Dang, Duy Minh
author_sort Dang, Duy Minh
title Modeling Multi-factor Financial Derivatives by a Partial Differential Equation Approach with Efficient Implementation on Graphics Processing Units
title_short Modeling Multi-factor Financial Derivatives by a Partial Differential Equation Approach with Efficient Implementation on Graphics Processing Units
title_full Modeling Multi-factor Financial Derivatives by a Partial Differential Equation Approach with Efficient Implementation on Graphics Processing Units
title_fullStr Modeling Multi-factor Financial Derivatives by a Partial Differential Equation Approach with Efficient Implementation on Graphics Processing Units
title_full_unstemmed Modeling Multi-factor Financial Derivatives by a Partial Differential Equation Approach with Efficient Implementation on Graphics Processing Units
title_sort modeling multi-factor financial derivatives by a partial differential equation approach with efficient implementation on graphics processing units
publishDate 2012
url http://hdl.handle.net/1807/42485
work_keys_str_mv AT dangduyminh modelingmultifactorfinancialderivativesbyapartialdifferentialequationapproachwithefficientimplementationongraphicsprocessingunits
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