Merton's Jump Diffusion Model

number of jumps

5

jump intensity

3

mean jump size

0

jump standard deviation

0.25

initial value

1

drift

0.5

volatility

0.1

number of steps

150

randomize

This Demonstration displays one path of Merton's "jump diffusion" stochastic process. This process extends the notion of the standard Black–Scholes model by allowing discrete jumps in addition to a Brownian process motion as the source of randomness. The jumps occur at random times. The interarrival times of the jumps follow an exponential distribution, while the size of the jumps has a normal distribution. Setting the mean size of jumps and the standard deviation to zero (the default) yields a path of a Black–Scholes process (exponential Wiener process).