Abstract: This paper mainly studies the convertible bonds pricing with instantaneous default risk under the Tsallis entropy and the Vasicek model. Under the premise that the stock price follows the Tsallis entropy distribution, building the portfolio and the partial differential equation satisfying the price of convertible bonds is obtained by the principle of no arbitrage. By using the finite element method, we can get the numerical solution of the price of convertible bonds. According to the market real data of the Changjiang Securities、Liou shares and Jilin Aodong shares, the Tsallis entropy distribution is used to simulate the yield sequence, and the optimal parameter of the stock price model based on the Tsallis entropy distribution is obtained. On this basis, we draw the three-dimensional graphs of theoretical prices of convertible bonds corresponding to three underlying stocks based on Tsallis entropy distribution and compare them with the actual market price. The results show that the theoretical price of the three securities convertible bonds based on Tsallis entropy distribution is closer to the market price.

Key words: convertible bond, Tsallis entropy, stochastic interest rate, instantaneous default risk, finite element method

摘要： 本文主要研究基于Tsallis熵分布且存在瞬时违约风险的情况下,随机利率服从Vasicek利率模型的可转换债券的定价问题。标的股票价格过程服从Tsallis熵分布的前提下,构建投资组合,利用无套利原理得到可转债价格所满足的偏微分方程,进一步采用有限元法得到可转债价格的数值解。根据长江证券、利欧股份以及吉林敖东股票的市场真实数据,利用Tsallis熵分布模拟收益率序列,并得到基于Tsallis熵分布的股价模型优于几何布朗运动模型下的最优参数,在此基础上,绘制股价基于Tsallis熵分布下三种标的股票所对应可转债的理论价格的三维图及与市场实际价格的对比图。研究结果发现,对应标的股票价格基于Tsallis熵分布下的可转债理论价格与市场真实价格更为接近。

关键词: 可转债, Tsallis熵分布, 随机利率, 瞬时违约风险, 有限元法