A Componentwise Splitting Method for Pricing American Options Under the Bates Model
A Componentwise Splitting Method for Pricing American Options Under the Bates Model
复制标题
贝茨模型下美式期权定价的成分分割法
DOI：
10.1007/978-90-481-3239-3_16
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
J. Toivanen
中科院分区：
文献类型：
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作者：
J. Toivanen
结合赫斯顿随机波动率模型和默顿跳-扩散模型的贝茨模型，提出了美式期权价格的线性互补问题。对偏导数采用有限差分离散化方法，对因跳跃引起的积分项采用简单的正交法。推广了贝茨模型的分块分割方法。这导致了一维lcp序列的求解，使用Brennan和Schwartz算法可以非常有效地求解。数值实验表明，该方法与PSOR方法基本相同，但速度快了一个数量级。此外，贝茨模型下的定价比实验中赫斯顿模型下的定价计算成本高出不到两倍。
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 jump-diffusion 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 one-dimensional 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.