9827

Merton's Jump Diffusion Model

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).

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The popular Black–Scholes model of the movement of stocks is known to be unsatisfactory for several reasons. A number of other models have been proposed that more accurately correspond to the observed behavior of stocks. One of the simplest such models is the Merton jump-diffusion model. The model adds to the Wiener process (which has continuous paths) a finite number of discrete jumps, whose times follow the Poisson distribution. In Merton's model, the size of the jumps is normally distributed. The jump intensity, jump mean size, and jump standard deviation affect the "jumping" aspects of the motion. The initial value, drift, volatility, and the number of steps used in simulating the continuous Wiener process. The "number of jumps" parameter essentially controls the duration of the process.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+