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摘要翻译：
本文用拟蒙特卡罗模拟方法研究了高维亚篮子期权的定价和套期保值问题。我们假设一个含时变挥发物的Black-Scholes市场，给出了如何借助Malliavin演算来计算增量，扩展了Montero和Kohatsu-Higa(2003)所采用的方法。有效的路径生成算法，如线性变换和主成分分析，在与时间相关的市场波动中表现出较高的计算代价。本文提出了一种新的快速的Cholesky算法，使得线性变换更加方便。此外，我们提出了一种基于Kronecker乘积近似的新路径生成技术。在相关资产收益的情况下，这种构造返回与用于计算增量和价格的线性变换相同的精度，同时要求较低的计算时间。所有这些技术都可以很容易地应用于Brigo等人提出的基于多维动力学混合的随机波动率模型。（2004年）。
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英文标题：
《Pricing and Hedging Asian Basket Options with Quasi-Monte Carlo
Simulations》
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作者：
Nicola Cufaro Petroni and Piergiacomo Sabino
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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：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：
In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by the aid of the Malliavin Calculus, extending the procedure employed by Montero and Kohatsu-Higa (2003). Efficient path-generation algorithms, such as Linear Transformation and Principal Component Analysis, exhibit a high computational cost in a market with time-dependent volatilities. We present a new and fast Cholesky algorithm for block matrices that makes the Linear Transformation even more convenient. Moreover, we propose a new-path generation technique based on a Kronecker Product Approximation. This construction returns the same accuracy of the Linear Transformation used for the computation of the deltas and the prices in the case of correlated asset returns while requiring a lower computational time. All these techniques can be easily employed for stochastic volatility models based on the mixture of multi-dimensional dynamics introduced by Brigo et al. (2004).
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PDF链接：
https://arxiv.org/pdf/0907.3092
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