# Distribution of Returns from Merton's Jump Diffusion Model

Distribution of Returns from Merton's Jump Diffusion Model

This Demonstration illustrates sample paths for an asset following Merton's jump diffusion model: the upper graph is a histogram of daily price returns, while the lower graph is the time series of price, both for a sample path of one year. The key feature of this model is that it incorporates large jumps; these show up as outliers in the histogram. The model parameters (namely, drift and volatility of the diffusive component, together with average size and volatility of the jumps) can be varied for a given sample. New random samples can be drawn, and the jump frequency (i.e., average number of jumps per sample) can be varied.