【作者】 孙毅；

【导师】 郑文瑞；

【作者基本信息】 吉林大学 ， 概率论与数理统计， 2016， 硕士

【摘要】 本文着重研究了彩虹亚式期权的定价问题。作为近几年金融市场中最受欢迎的奇异期权之一,基于维纳过程(Wiener process)的彩虹亚式期权的定价公式早就在[5]中给出,但是由于其定价公式中的参数选择过于死板,该公式并没有在实际投资过程中得到足够的重视。注意到此问题,我们假设其定价公式中所有参数,包括无风险利率,波动率和不同标的资产之间的相关系数,均为模糊数,并且基于Liu过程(参考[11]),从而建立了模糊彩虹亚式期权的定价模型。由于实际金融市场是会随时间而波动的,我们有理由相信我们得建立的模型会在实际金融市场中得到获得更好的成功。在模糊参数的假设下,彩虹看涨或看跌亚式期权的价格均相应地变为一个模糊数。然后我们应用[17]中提出的模糊集合理论分析了该模糊数的上下界。该工作将为那些做金融研究的金融研究员们选择合适的信赖等级的亚式期权价格提供直接帮助。据我们所知,我们的工作是具有开创性的,目前还没有研究彩虹亚式看涨或者看跌亚式期权模糊模糊定价上下界的相应文献。更多还原

【Abstract】 This paper focused on the pricing problem of Rainbow Asian Option. As one of the most popular exotic options in financial market in recent years, the pricing formula of Rainbow Asian Option was already constructed in [11] based on Wiener process, but suffering the rigidity of the choice of parameters, this formula has not gotten as much attention in the application in real investment.Noting this problem, we assume all these parameters including the risk-free interest rate, volatility and correlations between different underlying stocks are fuzzy numbers, and based on Liu process(see [5]), we proposed the fuzzy pricing model for Rainbow Asian Option. Our model is more proper to the real market, as the financial market is fluctuation from time to time. Therefore, we believe that our model can achieve great successes in the real financial market.Under the fuzzy parameters assumptions, the Rainbow call and put Asian Option price will turn into a fuzzy numbers. Then we used fuzzy sets theory as proposed in [17] to analyse the lower and upper bound such fuzzy number.This will make the financial analyst who can pick any reasonable Rainbow Asian Option price with an acceptable belief degree for his/her later financial analysis. As we can know, our work is pioneering, there is no literature analysing the bound of the fuzzy Rainbow Asian Call and Put Option price before.更多还原