英文标题：
《Quantum Bounds for Option Prices》
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作者：
Paul McCloud
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最新提交年份：
2018
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英文摘要：
  Option pricing is the most elemental challenge of mathematical finance. Knowledge of the prices of options at every strike is equivalent to knowing the entire pricing distribution for a security, as derivatives contingent on the security can be replicated using options. The available data may be insufficient to determine this distribution precisely, however, and the question arises: What are the bounds for the option price at a specified strike, given the market-implied constraints?   Positivity of the price map imposed by the principle of no-arbitrage is here utilised, via the Gelfand-Naimark-Segal construction, to transform the problem into the domain of operator algebras. Optimisation in this larger context is essentially geometric, and the outcome is simultaneously super-optimal for all commutative subalgebras.   This generates an upper bound for the price of a basket option. With innovative decomposition of the assets in the basket, the result is used to create converging families of price bounds for vanilla options, interpolate the volatility smile, price options on cross FX rates, and analyse the relationships between swaption and caplet prices.
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中文摘要：
期权定价是数学金融学最基本的挑战。了解每次行权时期权的价格相当于了解证券的整个定价分布，因为依赖于证券的衍生品可以使用期权进行复制。然而，现有的数据可能不足以精确地确定这种分布，因此产生了一个问题：考虑到市场隐含的约束，在特定的行使中，期权价格的界限是什么？这里，通过Gelfand-Naimark-Segal构造，利用无套利原则施加的价格图的正性，将问题转化为算子代数域。在这个更大的背景下，优化本质上是几何优化，并且对于所有交换子代数，结果同时是超最优的。这将生成一篮子期权价格的上限。通过对篮子中资产的创新分解，结果用于创建普通期权价格边界的收敛族，插值波动率微笑，交叉外汇利率上的价格期权，并分析互换期权和caplet价格之间的关系。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics        数学
二级分类：Operator Algebras        算子代数
分类描述：Algebras of operators on Hilbert space, C^*-algebras, von Neumann algebras, non-commutative geometry
Hilbert空间上算子的代数，C^*-代数，von Neumann代数，非交换几何
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