摘要翻译：
我们研究了Buchen-Kelly密度在一族熵最大密度中的位置，这些熵最大密度都与市场上观察到的给定到期日的欧式看涨期权价格相匹配。利用联系熵函数和累积量母函数的Legendre变换，证明了它既是该族中唯一的连续密度，又是熵最大的连续密度。本文提出了一种快速求根算法，可用于计算Buchen-Kelly密度，并给出了三种不同差异的上界作为收敛准则。给定看涨价格，相同罢工的无套利数字价格只能在左右看涨价差给定的上下边界内移动。随着呼叫价格数量的增加，这些界限变得更紧，我们给出了两个例子，当我们使用中心呼叫价差作为数字价格的代理时，密度收敛到相对熵意义下的Buchen-Kelly密度。正如Breeden和Litzenberger所指出的，在极限中，一组连续的看涨价格完全决定了密度。
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英文标题：
《A Family of Maximum Entropy Densities Matching Call Option Prices》
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作者：
Cassio Neri and Lorenz Schneider
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最新提交年份：
2011
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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 investigate the position of the Buchen-Kelly density in a family of entropy maximising densities which all match European call option prices for a given maturity observed in the market. Using the Legendre transform which links the entropy function and the cumulant generating function, we show that it is both the unique continuous density in this family and the one with the greatest entropy. We present a fast root-finding algorithm that can be used to calculate the Buchen-Kelly density, and give upper boundaries for three different discrepancies that can be used as convergence criteria. Given the call prices, arbitrage-free digital prices at the same strikes can only move within upper and lower boundaries given by left and right call spreads. As the number of call prices increases, these bounds become tighter, and we give two examples where the densities converge to the Buchen-Kelly density in the sense of relative entropy when we use centered call spreads as proxies for digital prices. As pointed out by Breeden and Litzenberger, in the limit a continuous set of call prices completely determines the density.
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PDF链接：
https://arxiv.org/pdf/1102.0224