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Componentwise splitting methods for pricing American options under stochastic volatility
 Int. J. Theor. Appl. Finance
, 2007
"... Abstract A linear complementarity problem (LCP) is formulated for the price of American options under the Bates model which combines the Heston stochastic volatility model and the Merton jumpdiffusion model. A finite difference discretization is described for the partial derivatives and a simple qu ..."
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Abstract A linear complementarity problem (LCP) is formulated for the price of American options under the Bates model which combines the Heston stochastic volatility model and the Merton jumpdiffusion model. A finite difference discretization is described for the partial derivatives and a simple quadrature is used for the integral term due to jumps. A componentwise splitting method is generalized for the Bates model. It is leads to solution of sequence of onedimensional LCPs which can be solved very efficiently using the Brennan and Schwartz algorithm. The numerical experiments demonstrate the componentwise splitting method to be essentially as accurate as the PSOR method, but order of magnitude faster. Furthermore, pricing under the Bates model is less than twice more expensive computationally than under the Heston model in the experiments. 1
Pricing American Options Using a Spacetime Adaptive Finite Difference Method
"... American options are priced numerically using a space and timeadaptive finite difference method. The generalized BlackScholes operator is discretized on a Cartesian structured but nonequidistant grid in space. The space and timediscretizations are adjusted such that a predefined tolerance level ..."
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Cited by 5 (1 self)
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American options are priced numerically using a space and timeadaptive finite difference method. The generalized BlackScholes operator is discretized on a Cartesian structured but nonequidistant grid in space. The space and timediscretizations are adjusted such that a predefined tolerance level on the local discretization error is met. An operator splitting technique is used to separately handle the early exercise constraint and the solution of linear systems of equations from the finite difference discretization of the linear complementarity problem. In numerical experiments three variants of the adaptive timestepping algorithm with and without local timestepping are compared.
An iterative method for pricing American options under jumpdiffusion models,
 Appl. Numer. Math.
, 2011
"... Abstract We consider the numerical pricing of American options under the Bates model which adds lognormally distributed jumps for the asset value to the Heston stochastic volatility model. A linear complementarity problem (LCP) is formulated where partial derivatives are discretized using finite d ..."
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Abstract We consider the numerical pricing of American options under the Bates model which adds lognormally distributed jumps for the asset value to the Heston stochastic volatility model. A linear complementarity problem (LCP) is formulated where partial derivatives are discretized using finite differences and the integral resulting from the jumps is evaluated using simple quadrature. A rapidly converging fixed point iteration is described for the LCP, where each iterate requires the solution of an LCP. These are easily solved using a projected algebraic multigrid (PAMG) method. The numerical experiments demonstrate the efficiency of the proposed approach. Furthermore, they show that the PAMG method leads to better scalability than the projected SOR (PSOR) method when the discretization is refined.
On the use of policy iteration as an easy way of pricing American options
 SIAM Journal on Financial Mathematics
"... Abstract. In this paper, we demonstrate that policy iteration, introduced in the context of HJB equations in [10], is an extremely simple generic algorithm for solving linear complementarity problems resulting from the finite difference and finite element approximation of American options. We show ..."
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Abstract. In this paper, we demonstrate that policy iteration, introduced in the context of HJB equations in [10], is an extremely simple generic algorithm for solving linear complementarity problems resulting from the finite difference and finite element approximation of American options. We show that, in general, O(N) is an upper and lower bound on the number of iterations needed to solve a discrete LCP of size N. If embedded in a class of standard discretisations with M time steps, the overall complexity of American option pricing is indeed only O(N(M +N)), and, therefore, for M ∼ N, identical to the pricing of European options, which is O(MN). We also discuss the numerical properties and robustness with respect to model parameters in relation to penalty and projected relaxation methods.
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, 2006
"... ���������������������� � ����������������������������������������������������� � Think different, think finite differences. From Sloganizer.netList of Papers This thesis is based on the following papers, which are referred to in the text by their Roman numerals. I J. Persson and L. von Sydow (2003). ..."
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���������������������� � ����������������������������������������������������� � Think different, think finite differences. From Sloganizer.netList of Papers This thesis is based on the following papers, which are referred to in the text by their Roman numerals. I J. Persson and L. von Sydow (2003). Pricing European Multiasset
Numerical Solution of Discretised HJB Equations with Applications in Finance
"... tesis no hubiese sido posible. Muchísimas gracias, amigo. Simplicity is the keynote of all true elegance. ..."
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tesis no hubiese sido posible. Muchísimas gracias, amigo. Simplicity is the keynote of all true elegance.
Original cover figures c○
"... CSC – Scientific Computing Ltd. is a nonprofit organization for highperformance computing and networking in Finland. CSC is owned by the Ministry of Education. CSC provides crossdisciplinary expertise, computational resources and fast network connections for computational science and engineering. ..."
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CSC – Scientific Computing Ltd. is a nonprofit organization for highperformance computing and networking in Finland. CSC is owned by the Ministry of Education. CSC provides crossdisciplinary expertise, computational resources and fast network connections for computational science and engineering. c ○ Authors and
AMERICAN OPTION PRICING UNDER STOCHASTIC VOLATILITY: A SIMULATIONBASED APPROACH
"... We consider the problem of pricing American options when the volatility of the underlying asset price is stochastic. No specific stochastic volatility model is assumed for the stochastic process. We propose a simulationbased approach to pricing such options. Iteratively, the method determines the o ..."
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We consider the problem of pricing American options when the volatility of the underlying asset price is stochastic. No specific stochastic volatility model is assumed for the stochastic process. We propose a simulationbased approach to pricing such options. Iteratively, the method determines the optimal exercise boundary and the associated price function for a general stochastic volatility model. Given an initial guess of the optimal exercise boundary, the Retrospective Approximation (RA) technique is used to calculate the associated value function. Using this function, the exercise boundary is improved and the process repeated till convergence. This method is a simulation based variant of the exercisepolicy improvement scheme developed in Chockalingam and Muthuraman (2007). An illustration of the method is provided when using the Heston (1993) model to represent the dynamics of the volatility, together with comparisons against existing methods to validate our numerical results. 1
Alexander Lipton
, 2013
"... Pricing of vanilla and first generation exotic options in the local stochastic volatility framework: survey and new results ..."
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Pricing of vanilla and first generation exotic options in the local stochastic volatility framework: survey and new results