英文标题：
《Implied volatility of basket options at extreme strikes》
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作者：
Archil Gulisashvili and Peter Tankov
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最新提交年份：
2014
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英文摘要：
In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the leading term of asymptotics of the implied volatility in the case where the asset prices follow the multidimensional Black-Scholes model with time change by an independent increasing stochastic process. Finally, we deal with a general situation in which the dependence between the assets is described by a given copula function. In this setting, we obtain a model-free tail-wing formula that links the implied volatility to a special characteristic of the copula called the weak lower tail dependence function.
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中文摘要：
在本文中，我们刻画了一篮子看涨期权在各种情况下的隐含波动率的渐近行为。首先，在假设资产价格的动态由多维Black-Scholes模型描述的情况下，我们得到了一个隐含波动率左翼有误差界的渐近公式。接下来，我们发现了在资产价格遵循多维Black-Scholes模型且随时间变化的情况下，通过一个独立的递增随机过程，隐含波动率的渐近性的前导项。最后，我们讨论了资产之间的依赖关系由给定的copula函数描述的一般情况。在这种情况下，我们得到了一个无模型尾翼公式，该公式将隐含波动率与copula的一个特殊特征联系起来，称为弱下尾依赖函数。
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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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