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雷达卡
摘要翻译：
一种有效的条件技术，即所谓的布朗桥模拟，以前曾被用于消除标准离散时间蒙特卡罗方法在评估标的资产的连续时间极值上的期权时出现的定价偏差。它是建立在一维布朗桥极值分布的简单易行的解析公式基础上的。本文将该技术推广到对所有或部分标的资产设置淘汰障碍的多资产期权的估值。推导了基于多维布朗桥相关极值联合分布的无偏期权价格估计量公式。由于一般情况下联合分布没有解析公式，我们基于独立极值分布和未知分布的上下界，建立了期权价格的上下有偏估计。所有估计量都很简单，易于实现。它们总是可以用来通过置信区间来绑定真值。数值试验表明，与基于标准离散时间方法的估计量相比，随着资产路径模拟时间步长的增加，我们的有偏估计量迅速收敛到真实的期权价值。收敛速度取决于基础资产的相关性和壁垒结构。
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英文标题：
《Addressing the bias in Monte Carlo pricing of multi-asset options with
multiple barriers through discrete sampling》
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作者：
P. V. Shevchenko
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最新提交年份：
2009
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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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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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英文摘要：
An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on the continuous-time extrema of an underlying asset. It is based on the simple and easy to implement analytic formulas for the distribution of one-dimensional Brownian Bridge extremes. This paper extends the technique to the valuation of multi-asset options with knock-out barriers imposed for all or some of the underlying assets. We derive formula for the unbiased option price estimator based on the joint distribution of the multi-dimensional Brownian Bridge dependent extrema. As analytic formulas are not available for the joint distribution in general, we develop upper and lower biased option price estimators based on the distribution of independent extrema and the Fr\'echet lower and upper bounds for the unknown distribution. All estimators are simple and easy to implement. They can always be used to bind the true value by a confidence interval. Numerical tests indicate that our biased estimators converge rapidly to the true option value as the number of time steps for the asset path simulation increases in comparison to the estimator based on the standard discrete-time method. The convergence rate depends on the correlation and barrier structures of the underlying assets.
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PDF链接：
https://arxiv.org/pdf/0904.1157
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