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

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