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英文标题：
《Valuation of Barrier Options using Sequential Monte Carlo》
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作者：
Pavel V. Shevchenko and Pierre Del Moral
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最新提交年份：
2015
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英文摘要：
Sequential Monte Carlo (SMC) methods have successfully been used in many applications in engineering, statistics and physics. However, these are seldom used in financial option pricing literature and practice. This paper presents SMC method for pricing barrier options with continuous and discrete monitoring of the barrier condition. Under the SMC method, simulated asset values rejected due to barrier condition are re-sampled from asset samples that do not breach the barrier condition improving the efficiency of the option price estimator; while under the standard Monte Carlo many simulated asset paths can be rejected by the barrier condition making it harder to estimate option price accurately. We compare SMC with the standard Monte Carlo method and demonstrate that the extra effort to implement SMC when compared with the standard Monte Carlo is very little while improvement in price estimate can be significant. Both methods result in unbiased estimators for the price converging to the true value as $1/\\sqrt{M}$, where $M$ is the number of simulations (asset paths). However, the variance of SMC estimator is smaller and does not grow with the number of time steps when compared to the standard Monte Carlo. In this paper we demonstrate that SMC can successfully be used for pricing barrier options. SMC can also be used for pricing other exotic options and also for cases with many underlying assets and additional stochastic factors such as stochastic volatility; we provide general formulas and references.
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中文摘要：
序贯蒙特卡罗（SMC）方法已成功地应用于工程、统计学和物理学等领域。然而，这些在金融期权定价文献和实践中很少使用。本文提出了一种对障碍条件进行连续和离散监测的障碍期权定价的SMC方法。在SMC方法下，由于障碍条件而被拒绝的模拟资产价值从不违反障碍条件的资产样本中重新取样，从而提高期权价格估计器的效率；而在标准蒙特卡罗下，许多模拟资产路径可能会被障碍条件拒绝，这使得更难准确估计期权价格。我们将SMC与标准Monte Carlo方法进行了比较，并证明了与标准Monte Carlo方法相比，实现SMC所需的额外努力非常少，而价格估计的改善可能是显著的。这两种方法都会使价格无偏估计值收敛到$1/\\sqrt{M}$的真实值，其中$M$是模拟的数量（资产路径）。然而，与标准蒙特卡罗方法相比，SMC估计的方差较小，且不随时间步长的增加而增加。在本文中，我们证明了SMC可以成功地用于障碍期权的定价。SMC还可用于其他奇异期权的定价，也可用于许多标的资产和其他随机因素（如随机波动性）的情况；我们提供一般公式和参考。
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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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