英文标题：
《Option Pricing with Heavy-Tailed Distributions of Logarithmic Returns》
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作者：
Lasko Basnarkov, Viktor Stojkoski, Zoran Utkovski and Ljupco Kocarev
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最新提交年份：
2019
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英文摘要：
A growing body of literature suggests that heavy tailed distributions represent an adequate model for the observations of log returns of stocks. Motivated by these findings, here we develop a discrete time framework for pricing of European options. Probability density functions of log returns for different periods are conveniently taken to be convolutions of the Student\'s t-distribution with three degrees of freedom. The supports of these distributions are truncated in order to obtain finite values for the options. Within this framework, options with different strikes and maturities for one stock rely on a single parameter -- the standard deviation of the Student\'s t-distribution for unit period. We provide a study which shows that the distribution support width has weak influence on the option prices for certain range of values of the width. It is furthermore shown that such family of truncated distributions approximately satisfies the no-arbitrage principle and the put-call parity. The relevance of the pricing procedure is empirically verified by obtaining remarkably good match of the numerically computed values by our scheme to real market data.
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中文摘要：
越来越多的文献表明，重尾分布是观察股票对数收益率的合适模型。基于这些发现，我们在此开发了欧洲期权定价的离散时间框架。不同时期对数收益的概率密度函数可以方便地看作是三自由度Student t分布的卷积。这些分布的支持被截断，以获得选项的有限值。在这个框架内，一只股票的不同行权和到期日的期权依赖于一个参数——单位周期内Student t分布的标准偏差。我们的研究表明，在一定的宽度范围内，分布支持宽度对期权价格的影响很校进一步证明了这种截断分布族近似满足无套利原则和看跌期权奇偶性。通过我们的方案获得的数值计算值与实际市场数据的非常好的匹配，实证验证了定价程序的相关性。
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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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