基于关联PIDE的价差合约定价的有限元策略
A Finite Elements Strategy for Spread Contract Valuation Via Associated PIDE
摘要：
本文研究了一种基于有限元的有效策略，通过求解相关的偏积分微分方程（PIDE），对标的资产服从二维Levy模型的商品价差期权进行定价。为此，我们考虑一个Galerkin近似的空间随着时间的演变的隐格式。扩散和漂移在相关的运营商离散使用精确的高斯求积，而对应于跳跃的积分部分近似使用最近在文献中介绍的符号方法。利用双共轭稳定梯度法（BICSTAB），在每个时间步引入一个循环预条件子，有效地求解了具有块Toeplitz块（BTTB）矩阵的方程组.该技术被应用到定价的\textit{crack}价差期权之间的期货RBOB汽油（重新配制的调合油）和西德克萨斯中质（WTI）石油在纽约商品交易所的价格。
英文摘要：
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.
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