Pricing multi-asset American options on Graphics Processing Units using a PDE approach

Dang, Duy Minh; Christara, Christina C.; Jackson, Kenneth R.

doi:10.1109/whpcf.2010.5671831

Cited by 5 publications

(3 citation statements)

References 14 publications

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“…Zhang and Oosterlee [29], Podlozhnyuk [24], Abbas-Turki and Lapeyre [5], Egloff [9], Joshi [12], and Dang et al [7] look at Black-Scholes pricing on the GPU, while Podlozhnyuk and Harris [25], Tian et al [28], Rees and Walkenhorst [26], Dixon et al [8], Pages and Wil-bertz [23], Bernemann et al [6], and Murakowski et al [15] look at GPU acceleration of Monte-Carlo for financial computation. Additional related work by Thomas [27] describes acceleration of Monte-Carlo using FPGAs.…”

Section: Related Workmentioning

confidence: 99%

Accelerating financial applications on the GPU

Grauer-Gray

Killian

Schleicher

et al. 2013

Proceedings of the 6th Workshop on General Purpose Processor Using Graphics Processing Units

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The QuantLib library is a popular library used for many areas of computational finance. In this work, the parallel processing power of the GPU is used to accelerate QuantLib financial applications. Black-Scholes, Monte-Carlo, Bonds, and Repo code paths in QuantLib are accelerated using hand-written CUDA and OpenCL codes specifically targeted for the GPU. Additionally, HMPP and OpenACC versions of the applications were created to drive the automatic generation of GPU code from sequential code. The results demonstrate a significant speedup for each code using each parallelization method. We were also able to increase the speedup of HMPP-generated code with auto-tuning.

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Section: Related Workmentioning

confidence: 99%

Accelerating financial applications on the GPU

Grauer-Gray

Killian

Schleicher

et al. 2013

Proceedings of the 6th Workshop on General Purpose Processor Using Graphics Processing Units

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“…

We present a graphics processing unit (GPU) parallelization of the computation of the price of exotic crosscurrency interest rate derivatives via a partial differential equation (PDE) approach. The literature on utilizing GPUs in pricing financial derivatives via a PDE approach is rather sparse, with scattered work presented at conferences or workshops, such as [7,14]. We consider a three-factor pricing model with FX volatility skew, which results in a time-dependent parabolic PDE in three spatial dimensions.

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mentioning

confidence: 99%

“…In the area of computational finance, although there has been great interest in utilizing GPUs in developing efficient pricing architectures for computationally intensive problems, the applications mostly focus on option pricing and MC simulations (e.g., [4][5][6]). The literature on utilizing GPUs in pricing financial derivatives via a PDE approach is rather sparse, with scattered work presented at conferences or workshops, such as [7,14]. The literature on GPU-based PDE methods for pricing cross-currency interest rate derivatives is even less developed.…”

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confidence: 99%

Graphics processing unit pricing of exotic cross‐currency interest rate derivatives with a foreign exchange volatility skew model

Dang

Christara

Jackson

2012

Concurrency and Computation

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We present a graphics processing unit (GPU) parallelization of the computation of the price of exotic crosscurrency interest rate derivatives via a partial differential equation (PDE) approach. In particular, we focus on the GPU-based parallel pricing of long-dated foreign exchange (FX) interest rate hybrids, namely power reverse dual currency (PRDC) swaps with Bermudan cancelable features. We consider a three-factor pricing model with FX volatility skew, which results in a time-dependent parabolic PDE in three spatial dimensions. Finite difference methods on uniform grids are used for the spatial discretization of the PDE, and the alternating direction implicit (ADI) technique is employed for the time discretization. We then exploit the parallel architectural features of GPUs together with the Compute Unified Device Architecture framework to design and implement an efficient parallel algorithm for pricing PRDC swaps. Over each period of the tenor structure, we divide the pricing of a Bermudan cancelable PRDC swap into two independent pricing subproblems, each of which can efficiently be solved on a GPU via a parallelization of the ADI timestepping technique. Numerical results indicate that GPUs can provide significant increase in performance over CPUs when pricing PRDC swaps. An analysis of the impact of the FX skew on such derivatives is provided. PRDC swaps. The use of a local volatility model provides better modeling for the skewness of the FX rate and at the same time avoids introducing more stochastic factors into the model.The ever growing interest in cross-currency interest rate derivatives in general, and PRDC swaps in particular, has created a need for efficient pricing and hedging strategies for them. The popular choice for pricing PRDC swaps is Monte-Carlo (MC) simulation, but this approach has several major disadvantages, including slow convergence, and the limitation that the price is obtained at a single point only in the domain as opposed to the global character of the partial differential equation (PDE) approach. In addition, accurate hedging parameters, such as delta and gamma, are generally harder to compute via an MC approach than via a PDE approach. On the other hand, when pricing PRDC swaps by the PDE approach, each stochastic factor in the pricing model gives rise to a spatial variable in the PDE. Because of the 'curse of dimensionality' associated with highdimensional PDEs-not to mention additional complexity due to multiple cash flows and exotic features, such as Bermudan cancelability-the pricing of such derivatives via the PDE approach is not only mathematically challenging but also very computationally intensive.Over the last few years, the rapid evolution of graphics processing units (GPUs) into powerful, cost efficient, programmable computing architectures for general purpose computations has provided application potential beyond the primary purpose of graphics processing. In the area of computational finance, although there has been great interest in utilizing GPUs in developing eff...

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