论文标题
通过关联的派对传播合同估值的有限元素策略
A Finite Elements Strategy for Spread Contract Valuation Via Associated PIDE
论文作者
论文摘要
我们研究了一种基于有限元素的有效策略，以将基本资产的基本资产估算为一定类别的二维征费模型所描述的动态，以衡量其相关的部分全差异方程（PIDE）。为此，我们考虑了空间中的Galerkin近似值以及时间演化的隐式方案。使用精确的高斯正交正常进行离散的相关操作员的扩散和漂移，而与跳跃相对应的积分部分是使用文献中最近引入的符号方法近似的。带有toeplitz块（BTTB）矩阵的封闭toeplitz的系统通过双轭稳定梯度法（BICSTAB）有效地求解，并在每个时间步骤中使用循环前的调节器。该技术适用于\ textit {crack}的定价，在Nymex中未来的RBOB汽油价格（用于氧合混合氧合的重新含量混合）和西德克萨斯中级油（WTI）的价格之间传播了选择。
We study an efficient strategy based on finite elements to value spread options on commodities whose underlying assets follow a dynamic described by a certain class of two-dimensional Levy models by solving their associated partial integro-differential equation (PIDE). To this end we consider a Galerkin approximation in space along with an implicit scheme for time evolution. Diffusion and drift in the associated operator are discretized using an exact Gaussian quadrature, while the integral part corresponding to jumps is approximated using the symbol method recently introduced in the literature. A system with blocked Toeplitz with Toeplitz blocks (BTTB) matrix is efficiently solved via biconjugate stabilized gradient method (BICSTAB) with a circulant pre-conditioner at each time step. The technique is applied to the pricing of \textit{crack} spread options between the prices of futures RBOB gasoline (reformulated blendstock for oxygenate blending) and West Texas Intermediate(WTI) oil in NYMEX.
