A fast numerical method for the valuation of American lookback put options
A fast numerical method for the valuation of American lookback put options
复制标题
美式回顾看跌期权估值的快速数值方法
DOI：
10.1016/j.cnsns.2015.03.010
复制
发表时间：
2015
影响因子：
3.9
通讯作者：
Zhang Ran
中科院分区：
文献类型：
--
作者：
Song Haiming;Zhang Qi;Zhang Ran
A fast and efficient numerical method is proposed and analyzed for the valuation of American lookback options. American lookback option pricing problem is essentially a two-dimensional unbounded nonlinear parabolic problem. We reformulate it into a two-dimensional parabolic linear complementary problem (LCP) on an unbounded domain. The numeraire transformation and domain truncation technique are employed to convert the two-dimensional unbounded LCP into a one-dimensional bounded one. Furthermore, the variational inequality (VI) form corresponding to the one-dimensional bounded LCP is obtained skillfully by some discussions. The resulting bounded VI is discretized by a finite element method. Meanwhile, the stability of the semi-discrete solution and the symmetric positive definiteness of the full-discrete matrix are established for the bounded VI. The discretized VI related to options is solved by a projection and contraction method. Numerical experiments are conducted to test the performance of the proposed method.
