Geodesic
Superconvergence estimates of finite element methods for American options
Applications of Mathematics, Tome 54 (2009) no. 3, pp. 181-202
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In this paper we are concerned with finite element approximations to the evaluation of American options. First, following W. Allegretto etc., SIAM J. Numer. Anal. {\it 39} (2001), 834--857, we introduce a novel practical approach to the discussed problem, which involves the exact reformulation of the original problem and the implementation of the numerical solution over a very small region so that this algorithm is very rapid and highly accurate. Secondly by means of a superapproximation and interpolation postprocessing analysis technique, we present sharp $L^2$-, $L^{\infty }$-norm error estimates and an $H^1$-norm superconvergence estimate for this finite element method. As a by-product, the global superconvergence result can be used to generate an efficient a posteriori error estimator.
In this paper we are concerned with finite element approximations to the evaluation of American options. First, following W. Allegretto etc., SIAM J. Numer. Anal. {\it 39} (2001), 834--857, we introduce a novel practical approach to the discussed problem, which involves the exact reformulation of the original problem and the implementation of the numerical solution over a very small region so that this algorithm is very rapid and highly accurate. Secondly by means of a superapproximation and interpolation postprocessing analysis technique, we present sharp $L^2$-, $L^{\infty }$-norm error estimates and an $H^1$-norm superconvergence estimate for this finite element method. As a by-product, the global superconvergence result can be used to generate an efficient a posteriori error estimator.
DOI : 10.1007/s10492-009-0012-x
Classification : 65K10, 65K15, 65M12, 65M60, 90A09, 91G10, 91G20, 91G60
Keywords: American options; variational inequality; finite element methods; optimal and superconvergent estimates; interpolation postprocessing; a posteriori error estimators 
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     title = {Superconvergence estimates of finite element methods for {American} options},
     journal = {Applications of Mathematics},
     pages = {181--202},
     year = {2009},
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Lin, Qun; Liu, Tang; Zhang, Shuhua. Superconvergence estimates of finite element methods for American options. Applications of Mathematics, Tome 54 (2009) no. 3, pp. 181-202. doi: 10.1007/s10492-009-0012-x

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