双分数跳-扩散环境下的可转换债券定价

Convertible Bonds Pricing in Bifractional Jump-diffusion Environment

可转换债券是一种兼具债券和期权特性的混合型高级金融衍生产品,其合理定价对发行人和投资者都具有重要的现实意义。在考虑企业市场价值波动和利率波动的基础上,假定股票价格遵循双分数Brown运动及跳过程驱动的随机微分方程,利率满足Vasicek模型,建立了双分数跳-扩散环境下的金融市场数学模型,利用双分数布朗运动的随机分析理论和保险精算方法,讨论了可转换债券定价问题,得到了双分数跳-扩散环境下的可转换债券定价公式,在现有研究的基础上对可转换债券定价公式进行了进一步的研究和推广,使模型更加贴近实际金融市场。

Convertible bond is a hybrid advanced financial derivatives with both features of bonds and options, and the reasonable pricing have important practical significance to issuers and investors. In this paper, on the basis of considering the volatility of enterprise market value and interest rates, assuming that stock price follows stochastic differential equations of bifractional Brownian motion and jumping process-driven, and the interest rate satisfies Vasicek model, the mathematical model of the financial market in the bifractional jump-diffusion environment is built. Using the stochastic analysis theory of bifractional Brownian motion and actuarial methods, the pricing problem of convertible bond is discussed, and the convertible bond pricing formula in bifractional jump-diffusion environment is obtained. On the basis of existing research the further research and promotion on convertible bonds pricing formula is done, so as to make the model more close to the actual finan- cial markets.