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摘要翻译：
利用Malliavin演算技术，我们导出了一个对于包括局部波动率和泊松跳跃过程的任意模型的欧式期权价格的解析公式。我们证明了该公式的精度取决于支付函数的光滑性。我们的方法依赖于一个与小扩散和小跳跃频率/尺寸相关的渐近展开。我们的公式具有很好的准确性（对于不同的罢工和到期日，看涨期权的隐含Black-Scholes挥发度误差小于2个bp）。此外，模型校准变得非常迅速。
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英文标题：
《Smart expansion and fast calibration for jump diffusion》
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作者：
Eric Benhamou (LJK), Emmanuel Gobet (LJK), Mohammed Miri (LJK)
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最新提交年份：
2008
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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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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of the payoff function. Our approach relies on an asymptotic expansion related to small diffusion and small jump frequency/size. Our formula has excellent accuracy (the error on implied Black-Scholes volatilities for call option is smaller than 2 bp for various strikes and maturities). Additionally, model calibration becomes very rapid.
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PDF链接：
https://arxiv.org/pdf/0712.3485
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