Knight不确定环境下基于模糊测度的期权定价模型  

Option Pricing with Fuzzy Measures under Knightian Uncertainty

作　　者：韩立岩[1] 周娟[1] 

机构地区：[1]北京航空航天大学经济管理学院,北京100083

出　　处：《系统工程理论与实践》2007年第12期123-132,共10页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(70671005)

摘　　要：传统微观金融学用唯一概率分布表示风险的存在,而Knight不确定性则不能被单一概率分布所揭示.Ellsberg悖论指出Knight不确定性的存在会影响当事人的行为选择进而影响资产价格.本文提出Knight不确定环境下期权定价模型,运用λ-模糊测度和Choquet积分求解欧式无红利期权的价格,所得期权价格是一个区间而不是某个特定数值,这与Epstein的基础资产结果在形式上是一致的;相应的实证研究结果表明:模糊测度参数λ的取值的确可以反映投资者个体的主观情绪,并且λ的变化能够反应投资个体的情绪变化.Conventionally we describe the risk with a unique probability measure. However, Ellsberg paradox indicates that the existing of Knightian uncertainty would have an effect on both decision-makers＇ behavior and asset pricing. In this paper we propose an option pricing model under Knightian uncertainty using the λ-fuzzy measure and the Choquet integral, and we get the equilibrium price of European option on a non-dividend-paying stock. The equilibrium price is an interval instead of a determinate number, which is in accordance with Epstein＇ s conclusion. Subsequently we do an empirical research and the outcome indicate that parameter λ which can describe human subjective sentimental will change with volatility of personal mood. Moreover, this will pave a new way to cope with other derivatives pricing under Knightian uncertainty.

关 键 词：KNIGHT不确定性 期权定价 λ-模糊测度 CHOQUET积分 

分 类 号：F830.9[经济管理—金融学]