基于跳扩散过程的可转换债券的定价

本文标的股票的方程采用跳扩散方程,首先规定一个跳跃的涨跌区间,这样就可以很快的找出跳跃点,我们根据跳跃点将股价聚类,然后把各个类看成是总体中抽取出来的一个样本,我们就可以估计出跳扩散方程中的所有参数.由于我们的标的股票的方程是含跳过程,因此无法找出完全保值的自融资策略,但我们可以根据风险最小化的原理给出可转换债券的价格,最后运用Monte Carlo模拟计算出了南京水运转债在0时刻的价格。

Pricing Convertible Bond Based on the Jump-diffusion Process

In this paper,we adopt the jump-diffusion equation as the underlying stock equation.First we set a fluctuating interval of stock price where the jump take place,so we can find the jump point easily.After that,we classify the stock prices according to the jump point,and every class is seen as a sample from the population,then we can estimate all the parameters of the jump-diffusion equation. Because our underlying stock equation is a one that including jump,so we cannot find a self-financing strategy that is completely hedged,but we can compute the price of convertible bond according to risk minimum principle.At last,Monte Carlo simulation is used for calculating the time 0 price of Nanjing Shuiyun.