英文标题：
《Learning Agents in Black-Scholes Financial Markets: Consensus Dynamics
and Volatility Smiles》
---
作者：
Tushar Vaidya and Carlos Murguia and Georgios Piliouras
---
最新提交年份：
2020
---
英文摘要：
Black-Scholes (BS) is the standard mathematical model for option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS framework assumes that volatility remains constant across all strikes, however, in practice it varies. How do traders come to learn these parameters? We introduce natural models of learning agents, in which they update their beliefs about the true implied volatility based on the opinions of other traders. We prove convergence of these opinion dynamics using techniques from control theory and leader-follower models, thus providing a resolution between theory and market practices. We allow for two different models, one with feedback and one with an unknown leader.
---
中文摘要：
Black-Scholes（BS）是金融市场期权定价的标准数学模型。期权价格使用一个分析公式进行计算，该公式的主要输入是履约（行使价格）和波动率。BS框架假设所有罢工期间的波动性保持不变，但在实践中有所不同。交易者是如何学习这些参数的？我们引入了学习主体的自然模型，在该模型中，学习主体根据其他交易者的意见更新其对真实隐含波动率的信念。我们使用控制理论和领导者-追随者模型的技术证明了这些意见动态的收敛性，从而提供了理论和市场实践之间的解决方案。我们考虑了两种不同的模型，一种是反馈模型，另一种是未知领导者模型。
---
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
--
一级分类：Computer Science 计算机科学
二级分类：Machine Learning 机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
--
一级分类：Computer Science 计算机科学
二级分类：Multiagent Systems 多智能体系统
分类描述：Covers multiagent systems, distributed artificial intelligence, intelligent agents, coordinated interactions. and practical applications. Roughly covers ACM Subject Class I.2.11.
涵盖多Agent系统、分布式人工智能、智能Agent、协调交互。和实际应用。大致涵盖ACM科目I.2.11类。
--

---
PDF下载：
-->