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首页> 外文会议>International Conference on Computational Science and Its Applications - ICCSA 2003 Pt.3 May 18-21, 2003 Montreal, Canada >Valuation of American Options Using Direct, Linear Complementarity-Based Methods
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Valuation of American Options Using Direct, Linear Complementarity-Based Methods

机译：使用直接，基于线性互补的方法对美式期权进行估值

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摘要

The Linear Complementarity Formulation of the American Option Valuation problem, which is based on the Black-Scholes partial differential operator, is often used to assist implicit solution methods. Taking advantage of numerical methods, we can obtain approximate solutions, where a "moving index" determines the approximate position of the moving boundary which corresponds to the optimal exercise boundary of the option. Both Direct Inverse Multiplication (DIM) and Stable DIM (SDIM) methods, which are presented in this paper, use the inverse of the coefficient matrix to locate the moving index and then solve a fixed boundary problem. DIM proves to be more than 100 times faster than very popular iterative competitors like Projected Successive OverRelax-ation (PSOR). Due to stability problems from which DIM suffers in some cases, a stable version of it, SDIM, has been proposed. Although SDIM is slightly slower than DIM, it is still much faster compared to PSOR.
机译：基于Black-Scholes偏微分算子的美国期权估值问题的线性互补公式，经常用于辅助隐式求解方法。利用数值方法，我们可以获得近似解，其中“运动指标”确定了与期权的最优行使边界相对应的运动边界的近似位置。本文提出的直接逆乘法（DIM）和稳定DIM（SDIM）方法都使用系数矩阵的逆来定位运动指标，然后解决固定边界问题。事实证明，DIM比非常流行的迭代竞争对手（如Projective Successive OverRelaxation）（PSOR）快100倍以上。由于在某些情况下DIM会遇到稳定性问题，因此已提出了其稳定版本SDIM。尽管SDIM比DIM稍慢，但与PSOR相比，它仍然快得多。

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