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Radial basis functions with partition of unity method for American options with stochastic volatility

(2019) COMPUTATIONAL ECONOMICS. 53(1). p.259-287
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Abstract
In this article, we price American options under Heston's stochastic volatility model using a radial basis function (RBF) with partition of unity method (PUM) applied to a linear complementary formulation of the free boundary partial differential equation problem. RBF-PUMs are local meshfree methods that are accurate and flexible with respect to the problem geometry and that produce algebraic problems with sparse matrices which have a moderate condition number. Next, a Crank-Nicolson time discretisation is combined with the operator splitting method to get a fully discrete problem. To better control the computational cost and the accuracy, adaptivity is used in the spatial discretisation. Numerical experiments illustrate the accuracy and efficiency of the proposed algorithm.
Keywords
Radial basis function, Partition of unity, Operator splitting, American option pricing, Stochastic volatility, Heston's model, PROBABILITY DENSITY-FUNCTION, DATA APPROXIMATION SCHEME, JUMP-DIFFUSION MODELS, EFFICIENT, MULTIQUADRICS, COLLOCATION, VALUATION, EQUATIONS

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Citation

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MLA
Mollapourasl, Reza, et al. “Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility.” COMPUTATIONAL ECONOMICS, vol. 53, no. 1, 2019, pp. 259–87.
APA
Mollapourasl, R., Fereshtian, A., & Vanmaele, M. (2019). Radial basis functions with partition of unity method for American options with stochastic volatility. COMPUTATIONAL ECONOMICS, 53(1), 259–287.
Chicago author-date
Mollapourasl, Reza, Ali Fereshtian, and Michèle Vanmaele. 2019. “Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility.” COMPUTATIONAL ECONOMICS 53 (1): 259–87.
Chicago author-date (all authors)
Mollapourasl, Reza, Ali Fereshtian, and Michèle Vanmaele. 2019. “Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility.” COMPUTATIONAL ECONOMICS 53 (1): 259–287.
Vancouver
1.
Mollapourasl R, Fereshtian A, Vanmaele M. Radial basis functions with partition of unity method for American options with stochastic volatility. COMPUTATIONAL ECONOMICS. 2019;53(1):259–87.
IEEE
[1]
R. Mollapourasl, A. Fereshtian, and M. Vanmaele, “Radial basis functions with partition of unity method for American options with stochastic volatility,” COMPUTATIONAL ECONOMICS, vol. 53, no. 1, pp. 259–287, 2019.
@article{8559493,
  abstract     = {In this article, we price American options under Heston's stochastic volatility model using a radial basis function (RBF) with partition of unity method (PUM) applied to a linear complementary formulation of the free boundary partial differential equation problem. RBF-PUMs are local meshfree methods that are accurate and flexible with respect to the problem geometry and that produce algebraic problems with sparse matrices which have a moderate condition number. Next, a Crank-Nicolson time discretisation is combined with the operator splitting method to get a fully discrete problem. To better control the computational cost and the accuracy, adaptivity is used in the spatial discretisation. Numerical experiments illustrate the accuracy and efficiency of the proposed algorithm.},
  author       = {Mollapourasl, Reza and Fereshtian, Ali and Vanmaele, Michèle},
  issn         = {0927-7099},
  journal      = {COMPUTATIONAL ECONOMICS},
  keywords     = {Radial basis function,Partition of unity,Operator splitting,American option pricing,Stochastic volatility,Heston's model,PROBABILITY DENSITY-FUNCTION,DATA APPROXIMATION SCHEME,JUMP-DIFFUSION MODELS,EFFICIENT,MULTIQUADRICS,COLLOCATION,VALUATION,EQUATIONS},
  language     = {eng},
  number       = {1},
  pages        = {259--287},
  title        = {Radial basis functions with partition of unity method for American options with stochastic volatility},
  url          = {http://dx.doi.org/10.1007/s10614-017-9739-8},
  volume       = {53},
  year         = {2019},
}

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