Abstract:

Using stochastic differential equation and Monte Carlo simulation, we established and verified a stock price model with Poisson jumps when the volatility obeyed CIR process. The price formula of stock was given and we also computed the mean and variance of stock yield. Numerical result indicates that the model can better reflect the characteristics of high kurtosis and fat tail of stock yields distribution.

Key words: stochastic volatility, compound Poisson process, CIR process, Monte Carlo exact simulation