RiskGBMJD

Description

RiskGBMJD generates a geometric Brownian motion with jump diffusion process with drift parameter , volatility parameter , jump rate , and normal parameters of jump size and .

This process is typically used in a financial context to model a return, such as the change in a stock price, when random shocks occur. Specifically, it is assumed that shocks occur according to a Poisson process with rate , and that at such times, there is a jump in the process that is normally distributed with parameters and .

Examples

RiskGBMJD(0.01, 0.05, 0.1, 0.015, 0.025, RiskTSTransform(1,0), RiskTSIntegrate(1,1)) generates a jump diffusion GBM process with drift 1%, volatility 5%, jump rate 0.1, jump mean 1.5%, and jump standard deviation 2.5%.

RiskGBMJD(C10, C11, C12, C13, C14, RiskTSTransform(1,0), RiskTSIntegrate(1,1)) specifies a jump diffusion geometric Brownian motion function with parameters taken from cells C10 to C14.

Technical Details

Define

= sample from a Normal(0,1) distribution

= sample from a Poisson distribution

Then for any ,  

Again, this is typically a model for the return of a security. The price is then found from , or equivalently, .