先验密度对最小相对熵密度的影响--基于SPX期权数据的实证研究
The Impact of the Prior Density on a Minimum Relative Entropy Density: A Case Study with SPX Option Data
摘要：
研究了如何找到与给定欧式看涨期权价格相匹配的概率密度问题。为了考虑关于这种密度的先验信息，我们将Neri和Schneider（2011）提出的算法推广到相对熵情况下，以找到资产价格的最大熵密度。这是适用于研究的影响，先验密度的选择，在两个市场的情况下。在第一种情况下，看涨期权的价格只在少数几次执行时被规定，我们可以看到，选择优先权，或者实际上忽略优先权，会产生明显不同的密度。第二种情况是CBOE期权价格数据给出的标准普尔500指数期权在大量的罢工。先验信息现在被认为是由校准的赫斯顿，Schoebel-Zhu或方差伽马模型。我们发现，由此产生的数字期权价格基本上是相同的（非相对）布肯-凯利密度本身。换句话说，在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，我们研究方差互换，并推导出一个简单的公式，公平方差互换率熵。然后，我们表明，再次，先验失去了公平方差互换率的影响，罢工的数量增加。
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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