英文标题：
《Error analysis in Fourier methods for option pricing》
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作者：
Fabi\\\'an Crocce, Juho H\\\"app\\\"ol\\\"a, Jonas Kiessling, Ra\\\'ul Tempone
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最新提交年份：
2015
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英文摘要：
We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential \\levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential equation that can be solved analytically in terms of the characteristic exponent of the \\levy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a novel bound for the error and use this bound to set the parameters for the numerical method. We analyse the properties of the bound for a dissipative and pure-jump example. The bound presented is independent of the asymptotic behaviour of option prices at extreme asset prices. The error bound can be decomposed into a product of terms resulting from the dynamics and the option payoff, respectively. The analysis is supplemented by numerical examples that demonstrate results comparable to and superior to the existing literature.
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中文摘要：
当标的资产遵循指数动态时，我们提供了使用傅里叶方法对欧式期权定价时所犯错误的界限。期权的价格由偏积分微分方程（PIDE）描述。将傅里叶变换应用于PIDE可产生一个常微分方程，该方程可根据莱维过程的特征指数进行解析求解。然后，通过数值逆傅里叶变换，我们可以得到期权价格。我们提出了一个新的误差界，并使用该界来设置数值方法的参数。我们分析了一个耗散纯跳跃例子的界的性质。给出的界限与极端资产价格下期权价格的渐近行为无关。误差界可以分解为分别由动态和期权收益产生的项的乘积。通过数值例子对分析进行了补充，证明了与现有文献相当且优于现有文献的结果。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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