We apply interior penalty discontinuous Galerkin finite element method (dGFEM) for pricing of European and American options for Heston PDE. The advantages of dGFEM space discretization with Rannacher smoothing as time integrator with non-smooth initial and boundary conditions are illustrated in several numerical examples for European call, as well as butterfly spread, digital call and American put options. The convection dominated Heston PDE for vanishing volatility is efficiently solved utilizing the adaptive dGFEM algorithm. The linear complementary problem for the American option is solved using the norm preconditioned projected successive over relaxation (PSOR) method. Numerical experiments illustrate that dGFEM is an accurate and efficient method for pricing options.

中文翻译：

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使用非连续伽辽金有限元在 Heston 模型下为欧美期权定价

我们应用内罚不连续伽辽金有限元法 (dGFEM) 为 Heston PDE 的欧洲和美国期权定价。dGFEM 空间离散化和 Rannacher 平滑作为时间积分器与非平滑初始和边界条件的优势在欧洲看涨期权、蝴蝶价差、数字看涨期权和美式看跌期权的几个数值例子中得到了说明。使用自适应 dGFEM 算法可以有效地解决对流主导的 Heston PDE 以消除波动性。美式期权的线性互补问题使用范数预处理投影连续过度松弛 (PSOR) 方法解决。数值实验表明，dGFEM 是一种准确有效的期权定价方法。