摘要
以欧式期权为例,用标的资产(如股票风险资产)和无风险资产复制期权,并用自融资无套利原理分析金融市场的资产价值变化情况.在此基础上,通过最大熵原理来求得资产组合中每个资产所占的比重,进而得出期权定价模型,由于最大熵原理所求得概率分布是目前所知求概率分布方法中最客观、无偏的,所以求得的新模型不受金融市场类型和标的资产价格分布的限制,具有较强的客观、无偏、可预测性.通过对期权的常用算例计算,发现新模型比B-S模型以及一些其它熵期权定价模型有更准确的标的资产价格分布、更低的回溯测试误差.
Considering the European option pricing, we use risk assets and risk-free assets to copy the European option, and combine further with self-financing and no-arbitrage theory to study the value of the portfolio in thesecurities market. ~rthermore, the probabilities distribution of risk assets and risk-free assets are obtained respectively by maximum entropy formalism and a novel model of the European option pricing is developed. As the maximum entropy criterion is one of the most objective and unbiased methods for finding probability distributions, the new model is independent of market types and underlying assets pricing distribution. Several typical numerical examples show that the new model has more accurate underlying assets pricing distribution, lower back-testing error than B-S model and some other entropy-based option pricing models.
出处
《数学的实践与认识》
CSCD
北大核心
2010年第5期30-36,共7页
Mathematics in Practice and Theory
基金
国家自然科学基金重大项目(10590354)
国家自然科学基金(10572031)
关键词
期权定价
最大熵原理
自融资
无套利原理
option pricing
maximum entropy formalism
self-financing portfolio
no-arbitrage theory
