摘要翻译：
我们提出了一个关于衍生品定价的概率框架，它承认信息和信念是主观的。市场价格可以转化为隐含的概率。特别是，期货隐含了这些隐含概率分布的回报。我们认为波动性不是风险，而是不确定性。非正态分布把左尾的风险和右尾的机会结合起来--把“风险溢价”和可能的损失统一起来。风险和回报必须是同一画面的一部分，预期回报必须包括因风险而可能造成的损失。我们将Black-Scholes定价公式重新解释为最大熵概率分布的价格，从一个新的角度说明了它们的重要性。利用这些思想，我们展示了衍生品如何在“不确定的不确定性”下定价，以及这是如何为隐含的挥发物造成倾斜的。我们认为，目前基于随机模型和风险中性定价的标准方法未能考虑到市场的主观性，并将不确定性错误地视为风险。此外，它建立在一个有问题的论点上--即不惜一切代价消除不确定性。
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英文标题：
《A Subjective and Probabilistic Approach to Derivatives》
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作者：
Ulrich Kirchner
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最新提交年份：
2010
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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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一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
  We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied probability distributions. We argue that volatility is not risk, but uncertainty. Non-normal distributions combine the risk in the left tail with the opportunities in the right tail -- unifying the "risk premium" with the possible loss. Risk and reward must be part of the same picture and expected returns must include possible losses due to risks. We reinterpret the Black-Scholes pricing formulas as prices for maximum-entropy probability distributions, illuminating their importance from a new angle. Using these ideas we show how derivatives can be priced under "uncertain uncertainty" and how this creates a skew for the implied volatilities. We argue that the current standard approach based on stochastic modelling and risk-neutral pricing fails to account for subjectivity in markets and mistreats uncertainty as risk. Furthermore, it is founded on a questionable argument -- that uncertainty is eliminated at all cost.
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PDF链接：
https://arxiv.org/pdf/1001.1616