Quantitative error estimates for a least-squares Monte Carlo algorithm for American option pricing
Quantitative error estimates for a least-squares Monte Carlo algorithm for American option pricing
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DOI：
10.1007/s00780-013-0204-9
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发表时间：
2013-04
影响因子：
1.7
通讯作者：
Daniel Z. Zanger
中科院分区：
文献类型：
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作者：
Daniel Z. Zanger
我们证明了新的误差估计的Longstaff-Schwartz算法。当算法的逼近结构是任意一组具有有限维Vapnik-Chervonenkis维数的L2函数时，我们建立了该算法的L2样本误差的收敛速度（其中N是Monte Carlo样本路径的数目）。此外，我们还将这些结果应用于多项式的有限维向量空间以及某些非线性神经网络集合所定义的逼近方案的情况。我们得到相应的估计，即使当基本的和支付过程不一定几乎必然有界。这些结果扩展并加强了Egloff（Ann. Appl. Probab. 15，1396-1432，2005），Egloff等人，(Ann.应用概率17，1138-1171，2007）、科勒（Kohler）等人（Math. Finance 20，383-410，2010）、格拉瑟曼（Glasserman）和于（Ann. Appl. Probab. 14，2090-2119，2004），Clément等人（Finance Stoch. 6，449-471，2002）以及其他。
We prove new error estimates for the Longstaff–Schwartz algorithm. We establish anconvergence rate for the expectedL2sample error of this algorithm (whereNis the number of Monte Carlo sample paths), whenever the approximation architecture of the algorithm is an arbitrary set ofL2functions with finite Vapnik–Chervonenkis dimension. Incorporating bounds on the approximation error as well, we then apply these results to the case of approximation schemes defined by finite-dimensional vector spaces of polynomials as well as that of certain nonlinear sets of neural networks. We obtain corresponding estimates even when the underlying and payoff processes are not necessarily almost surely bounded. These results extend and strengthen those of Egloff (Ann. Appl. Probab. 15, 1396–1432, 2005), Egloff et al. (Ann. Appl. Probab. 17, 1138–1171, 2007), Kohler et al. (Math. Finance 20, 383–410, 2010), Glasserman and Yu (Ann. Appl. Probab. 14, 2090–2119, 2004), Clément et al. (Finance Stoch. 6, 449–471, 2002) as well as others.