Option Prices in Merton's Jump Diffusion Model
Option Prices in Merton's Jump Diffusion Model
The jump diffusion model, introduced in 1976 by Robert Merton, is a model for stock price behavior that incorporates small day-to-day "diffusive" movements together with larger, randomly occurring "jumps". The inclusion of jumps allows for more realistic "crash" scenarios and means that the standard dynamic replication hedging approach of the standard Black-Scholes model no longer works. This causes option prices to increase compared to the Black-Scholes model and to depend on the risk aversion of investors. This Demonstration explores how the price of European call and put options varies with the jump diffusion model parameters.