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摘要翻译：
我们考虑了一篮子基础资产的路径依赖期权的定价问题。作为一个例子，我们使用亚式期权来发展我们的研究。亚式期权是一种衍生品合约，其基础变量是在一段时间内抽样的给定资产的平均价格。由于这种结构，亚洲期权表现出较低的波动性，因此比标准的欧洲期权更便宜。本文综述了近年来在Black-Scholes模型中用Monte Carlo模拟定价亚式期权时的一些改进，以提高定价效率。我们分析了基础资产收益在不变和随时间变化的情况下的动态变化。本文比较了标准蒙特卡罗方法(MC)和分层拉丁超立方抽样(LHS)的精度。特别地，我们讨论了低差异序列的使用，也称为拟蒙特卡罗方法(QMC)和这些序列的随机版本，称为随机拟蒙特卡罗(RQMC)。后者已被证明是一种有用的方差减少技术，既适用于高达20维的问题，也适用于非常高维的问题。此外，我们提出并测试了一种新的基于Kronecker乘积近似(KPA)的路径生成方法。证明了KPA是一种快速生成技术，并降低了模拟过程的计算代价。
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英文标题：
《Monte Carlo Methods and Path-Generation techniques for Pricing
Multi-asset Path-dependent Options》
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作者：
Piergiacomo Sabino (Dipartimento di Matematica, Universit\`a degli
Studi di Bari)
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最新提交年份：
2007
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分类信息：
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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一级分类：Statistics 统计学
二级分类：Applications 应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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英文摘要：
We consider the problem of pricing path-dependent options on a basket of underlying assets using simulations. As an example we develop our studies using Asian options. Asian options are derivative contracts in which the underlying variable is the average price of given assets sampled over a period of time. Due to this structure, Asian options display a lower volatility and are therefore cheaper than their standard European counterparts. This paper is a survey of some recent enhancements to improve efficiency when pricing Asian options by Monte Carlo simulation in the Black-Scholes model. We analyze the dynamics with constant and time-dependent volatilities of the underlying asset returns. We present a comparison between the precision of the standard Monte Carlo method (MC) and the stratified Latin Hypercube Sampling (LHS). In particular, we discuss the use of low-discrepancy sequences, also known as Quasi-Monte Carlo method (QMC), and a randomized version of these sequences, known as Randomized Quasi Monte Carlo (RQMC). The latter has proven to be a useful variance reduction technique for both problems of up to 20 dimensions and for very high dimensions. Moreover, we present and test a new path generation approach based on a Kronecker product approximation (KPA) in the case of time-dependent volatilities. KPA proves to be a fast generation technique and reduces the computational cost of the simulation procedure.
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PDF链接：
https://arxiv.org/pdf/710.085
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