Linking Vanillas and VIX Options: A Constrained Martingale Optimal Transport Problem
Linking Vanillas and VIX Options: A Constrained Martingale Optimal Transport Problem
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连接普通期权和 VIX 期权：受限鞅最优传输问题
DOI：
10.2139/ssrn.2354898
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
P. Henry
中科院分区：
文献类型：
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作者：
S. Marco;P. Henry
在芝加哥期权交易所交易的波动率指数期权已成为流行的波动率衍生品。由于标准普尔500指数的普通期权和波动率指数都取决于标准普尔500指数的波动动态，因此了解这些产品之间的联系非常重要。在本文中，我们绑定VIX期权从香草期权和VIX期货。这使我们引入一个新的鞅最优运输问题，我们解决数值。还提供了分析下限和上限，其中已经突出了一些（潜在的）套利机会。我们充分刻画了一类边际分布，这些明确的界限是最佳的，并说明数字，他们似乎是最佳的市场隐含的边际分布。
VIX options traded on the CBOE have become popular volatility derivatives. As S&P 500 vanilla options and VIX both depend on S&P 500 volatility dynamics, it is important to understand the link between these products. In this paper, we bound VIX options from vanilla options and VIX futures. This leads us to introduce a new martingale optimal transportation problem that we solve numerically. Analytical lower and upper bounds are also provided which already highlight some (potential) arbitrage opportunities. We fully characterize the class of marginal distributions for which these explicit bounds are optimal, and illustrate numerically that they seem to be optimal for the market-implied marginal distributions.