英文标题：
《Some Contributions to Sequential Monte Carlo Methods for Option Pricing》
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作者：
Deborshee Sen, Ajay Jasra and Yan Zhou
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最新提交年份：
2016
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英文摘要：
Pricing options is an important problem in financial engineering. In many scenarios of practical interest, financial option prices associated to an underlying asset reduces to computing an expectation w.r.t.~a diffusion process. In general, these expectations cannot be calculated analytically, and one way to approximate these quantities is via the Monte Carlo method; Monte Carlo methods have been used to price options since at least the 1970\'s. It has been seen in Del Moral, P. \\& Shevchenko, P.V. (2014) `Valuation of barrier options using Sequential Monte Carlo\' and Jasra, A. \\& Del Moral, P. (2011) `Sequential Monte Carlo for option pricing\' that Sequential Monte Carlo (SMC) methods are a natural tool to apply in this context and can vastly improve over standard Monte Carlo. In this article, in a similar spirit to Del Moral, P. \\& Shevchenko, P.V. (2014) `Valuation of barrier options using sequential Monte Carlo\' and Jasra, A. \\& Del Moral, P. (2011) `Sequential Monte Carlo for option pricing\' we show that one can achieve significant gains by using SMC methods by constructing a sequence of artificial target densities over time. In particular, we approximate the optimal importance sampling distribution in the SMC algorithm by using a sequence of weighting functions. This is demonstrated on two examples, barrier options and target accrual redemption notes (TARN\'s). We also provide a proof of unbiasedness of our SMC estimate.
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中文摘要：
期权定价是金融工程中的一个重要问题。在许多具有实际意义的场景中，与标的资产相关的金融期权价格简化为计算期望w.r.t.~扩散过程。一般来说，这些期望值无法通过分析计算得出，估计这些量的一种方法是通过蒙特卡罗方法；至少从20世纪70年代起，蒙特卡罗方法就被用于期权定价。这在Del Moral，P.\\&Shevchenko，P.V.（2014）`使用顺序蒙特卡罗对障碍期权进行估价\'和Jasra，A.\\&Del Moral，P.（2011）《期权定价的序贯蒙特卡罗》（Sequential Monte Carlo for option pricing）指出，序贯蒙特卡罗（SMC）方法是在这种情况下应用的自然工具，可以大大改进标准蒙特卡罗方法。在本文中，本着与Del Moral，P.\\&Shevchenko，P.V.（2014）`使用序贯蒙特卡罗对障碍期权进行估值\'和Jasra，a.\\&Del Moral，P.（2011）`期权定价的序贯蒙特卡罗\'类似的精神，我们表明，通过构建一系列随时间变化的人工目标密度，使用SMC方法可以获得显著收益。特别地，我们通过使用一系列加权函数来近似SMC算法中的最优重要性抽样分布。这在障碍期权和目标应计赎回票据（TARN）两个示例中得到了证明。我们还提供了SMC估计无偏的证明。
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分类信息：

一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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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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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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