英文标题：
《Application of Operator Splitting Methods in Finance》
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作者：
Karel in \'t Hout, Jari Toivanen
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最新提交年份：
2015
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英文摘要：
Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or multidimensional parabolic problems of the convection-diffusion type and generalizations thereof. An overview of various operator splitting methods is presented for the efficient numerical solution of these problems. Splitting schemes of the Alternating Direction Implicit (ADI) type are discussed for multidimensional problems, e.g. given by stochastic volatility (SV) models. For jump models Implicit-Explicit (IMEX) methods are considered which efficiently treat the nonlocal jump operator. For American options an easy-to-implement operator splitting method is described for the resulting linear complementarity problems. Numerical experiments are presented to illustrate the actual stability and convergence of the splitting schemes. Here European and American put options are considered under four asset price models: the classical Black-Scholes model, the Merton jump-diffusion model, the Heston SV model, and the Bates SV model with jumps.
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中文摘要：
金融衍生工具定价的目的是确定标的资产的金融合同的公允价值。这里我们考虑偏微分方程框架下的期权定价。当代模型导致对流扩散型的一维或多维抛物问题及其推广。为了有效地数值求解这些问题，本文综述了各种算子分裂方法。本文讨论了多维问题的交替方向隐式（ADI）分裂格式，例如由随机波动率（SV）模型给出的分裂格式。对于跳跃模型，考虑了有效处理非局部跳跃算子的隐-显（IMEX）方法。对于美式期权，描述了一种易于实现的算子分裂方法，用于求解由此产生的线性互补问题。数值实验证明了分裂格式的稳定性和收敛性。在这里，欧洲和美国的看跌期权被考虑在四种资产价格模型下：经典的Black-Scholes模型、Merton跳跃扩散模型、Heston SV模型和带跳跃的Bates SV模型。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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