跳扩散模型下的可转债定价—基于多叉树方法

Pricing convertible bonds under a jump diffusion model based on a multi-tree approach

  • 摘要: 可转债是兼具债券、股票和期权多重特性的派生金融产品, 其定价研究受到越来越多的关注. 利用一种新型多叉树模型拟合的跳跃扩散过程描述股价变动, 推导了相应的可转债定价迭代公式. 从数值计算结果看, 该多叉树模型收敛速度较快, 定价偏差较小. 与蒙特卡洛模拟方法相比, 该多叉树模型在准确性、运行效率等方面均有优势. 从模型主要参数的敏感性分析来看, 可转债价值受转股价和股价波动性影响显著, 股价跳跃波动越高导致可转债价值越高.

     

    Abstract: Convertible bonds are derivative financial products with multiple investment characteristics of bonds, stocks and options, and their pricing research has received more and more attention. We use the jump-diffusion process to describe the dynamics of stock price, and introduce the HS tree model to derive the corresponding iterative formulas of convertible bond’s price. Our results show that the convergence speed of the HS model is high and the deviation of the estimator is small. Compared with Monte Carlo simulation, the HS tree model has advantages in accuracy and efficiency. From the sensitivity analysis, the price of the convertible bond is significantly affected by the conversion price and the volatility of the stock’s price. The higher the volatility of the stock’s price is, the higher the value of the convertible bond is.

     

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