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Convergence analysis of CrankNicolson and Rannacher timemarching
 J. Comput. Finance
"... This paper presents a convergence analysis of Crank–Nicolson and Rannacher timemarching methods which are often used in finite difference discretizations of the Black–Scholes equations. Particular attention is paid to the important role of Rannacher’s startup procedure, in which one or more initial ..."
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Cited by 19 (1 self)
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This paper presents a convergence analysis of Crank–Nicolson and Rannacher timemarching methods which are often used in finite difference discretizations of the Black–Scholes equations. Particular attention is paid to the important role of Rannacher’s startup procedure, in which one or more initial timesteps use backward Euler timestepping, to achieve secondorder convergence for approximations of the first and second derivatives. Numerical results confirm the sharpness of the error analysis which is based on asymptotic analysis of the behavior of the Fourier transform. The relevance to Black–Scholes applications is discussed in detail, with numerical results supporting recommendations on how to maximize the accuracy for a given computational cost. 1
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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Cited by 8 (0 self)
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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
equation with Dirac
, 2004
"... Sharp error estimates for discretizations of the 1D convection–diffusion ..."
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An efficient method for pricing american options for jump diffusions, http://arxiv.org/abs/0706.2331
, 2007
"... We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating sequence solves an optimal stopping problem for geometric Bro ..."
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We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating sequence solves an optimal stopping problem for geometric Brownian motion, and can be numerically constructed using the classical finite difference methods. We present examples to illustrate our algorithm’s numerical performance.
Quantitative Finance
, 2009
"... Part of the Finance and Financial Management Commons, and the Mathematics Commons This Article is brought to you for free and open access by the School of Mathematics at ..."
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Part of the Finance and Financial Management Commons, and the Mathematics Commons This Article is brought to you for free and open access by the School of Mathematics at