【作者】 李飞；

【导师】 李绍文；

【作者基本信息】 西南财经大学 ， 数理金融学， 2019， 硕士

【摘要】 许多实证研究显示:随时间波动的利率对于金融市场中期权的价格变化有重要影响,同时,对金融市场中突发事件的产生及其对股价影响的刻画也是优异的定价模型不可或缺的因素,而跳扩散模型就能实现对突发事件的较好刻画。所以,基于对前人研究成果的总结,本文将跳扩散过程与随机利率相结合,构建欧式期权的定价模型。另外,以往对期权定价模型进行求解的方法往往选取傅里叶变换方法,近些年部分学者的研究表明运用Mellin变换方法可以有效减少计算复杂程度,比传统解答方法更为简便。基于此,本文首先利用Mellin变换的方法得到了几何布朗运动下带有固定利率的的欧式期权解析解的形式,根据Feynman-Kac方程得出期权价格满足的偏微分方程,再利用Mellin变换对方程进行转换求解;然后放宽约束条件,假设利率服从Hull-White模型,利用Mellin变换的方法得到了跳扩散过程下带有随机利率的欧式期权定价公式,并用数值案例分析了参数对期权价值的影响,其结果较为理想,最后还对利率模型进行深化推广,对带有跳风险的利率模型进行研究,得到其期权定价公式。更多还原

【Abstract】 Many empirical studies show that the interest rate fluctuating over time has an important influence on the price change of options in the financial market,at the same time,the description of the emergence of emergencies in the financial market and their influence on the stock price is also an indispensable factor for an excellent pricing model.Based on the summary of previous research,this paper combines jump-diffusion process with stochastic interest rate to build a new pricing model of European options.Meanwhile,in recent years,many articles have shown that Mellin transform method can reduce the computational complexity compared with the traditional probability method,and is increasingly favored by scholars in option pricing practices.Based on this,we assume that the stock price obeys the geometric Brown motion,we first use the Mellin transform to obtain the form of the analytic solution of European options with fixed interest rate under jump-diffusion process.Then we loosen constraints,assume the interest rate follows Hull-White model.We also discuss the case when interest rate follows jump-diffusion process.By using the method of Mellin transform we get the pricing formula of European option under stochastic interest rate under jump-diffusion process.Through Mellin transform method,we can simplify the complex option pricing problem and get its solution,which provides a new method for option pricing research.The influence of the parameters on the option value is analyzed with a numerical example.更多还原