摘要翻译：
我们研究了寻找与给定欧式看涨期权价格相匹配的概率密度的问题。为了考虑关于这种密度的先验信息，我们将Neri和Schneider(2011)中提出的求资产价格最大熵密度的算法推广到相对熵情况。这被应用于研究在两个市场场景中先验密度的选择所产生的影响。在第一种情况下，看涨期权的价格只规定在少量的罢工时，我们看到选择先验，或者实际上不选择先验，会产生明显不同的密度。第二种情况是由CBOE的S&P500指数期权价格数据给出的。先验信息现在被认为是由校准的Heston、Schoebel-Zhu或方差伽马模型给出的。我们发现由此产生的数字期权价格与由（非相对的）Buchen-Kelly密度本身给出的价格本质上是相同的。换句话说，在一个流动性充足的市场中，先验密度的影响似乎几乎完全消失。最后，我们研究了方差互换，导出了公平方差互换率与熵的一个简单关系式。然后，我们再一次证明，随着罢工次数的增加，先验对公平方差互换率的影响消失了。
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英文标题：
《The Impact of the Prior Density on a Minimum Relative Entropy Density: A
  Case Study with SPX Option Data》
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作者：
C. Neri (Lloyds Banking Group, London, UK), L. Schneider (EMLYON
  Business School, Lyon, France)
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最新提交年份：
2013
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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：
  We study the problem of finding probability densities that match given European call option prices. To allow prior information about such a density to be taken into account, we generalise the algorithm presented in Neri and Schneider (2011) to find the maximum entropy density of an asset price to the relative entropy case. This is applied to study the impact the choice of prior density has in two market scenarios. In the first scenario, call option prices are prescribed at only a small number of strikes, and we see that the choice of prior, or indeed its omission, yields notably different densities. The second scenario is given by CBOE option price data for S&P500 index options at a large number of strikes. Prior information is now considered to be given by calibrated Heston, Schoebel-Zhu or Variance Gamma models. We find that the resulting digital option prices are essentially the same as those given by the (non-relative) Buchen-Kelly density itself. In other words, in a sufficiently liquid market the influence of the prior density seems to vanish almost completely. Finally, we study variance swaps and derive a simple formula relating the fair variance swap rate to entropy. Then we show, again, that the prior loses its influence on the fair variance swap rate as the number of strikes increases.
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PDF链接：
https://arxiv.org/pdf/1201.2616