Affiliations: [a] Department of Mathematical Sciences, Tsinghua University, Beijing, China
| [b] School of Mathematics, Renmin University of China, Beijing, China
Correspondence:
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Corresponding author. Wenfei Li, School of Mathematics, Renmin University of China, Beijing 100872, China. E-mail: th19@mails.tsinghua.edu.cn.
Abstract: Interest rate, stock and option are all important parts of finance. This paper applies uncertain differential equation to the study of the evolution of interest rate and stock price separately. Based on actual observations, we estimate the parameters in uncertain differential equation with the method of moments. Using the introduced interest rate and stock models, we price European options and compare the results with actual observations. Finally, a paradox of the stochastic financial model is stated.
Keywords: Uncertain differential equation, geometric Liu process, uncertain exponential Ornstein-Uhlenbeck process, parameter estimation, European option pricing
