Sign up ×
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It's 100% free, no registration required.

I have simulated one possible path of a variance gamma process by the following code:





for (i in 2:23){
randomgamma<-rgamma(1, shape=1/v, scale = v)


The idea is to be found on page 26 in the following paper:

Now my problem is, that the plot does not look like a variance gamma process, these should look like this:

or this demonstration.

So where is my mistake?

In general: Is what I am doing correct? I want to simulate a stock path. The initial value of the stock is 20. Now, I want to simulate different paths. What parameters should I use to get a realistic result?

share|improve this question
first of all, there are 3 different methods on that page, which are you attempting? – jerad Nov 25 '12 at 22:15
also, what's your plot look like? – jerad Nov 25 '12 at 22:20
I noticed an edit to this post in reply to @jerad's comments (indicating the 1st method was considered). If you lost your account information, please flag your post for moderator attention and we will merge your accounts. – chl Nov 26 '12 at 8:31

2 Answers 2

I am using the variance gamma as well, and I just plotted it using the same algorithm implemented in R (which is what you use as well I guess). Simply change your 8th line of code as follows:

randomgamma<-rgamma(1, shape=1/v, scale = 1/v)

The issue with your code is the scale parameter. The scale parameter in the algorithm you refer to was meant to be a 'rate parameter' instead of a frequency parameter. However, R only interprets it as a frequency type of parameter. Good luck.

share|improve this answer
Forgot to add that if you make the suggested modification you should choose small values of v(.01 .001 ...) otherwise you wont have many jumps as in the wikipedia pictures. – PATCAT Jun 23 '14 at 6:30
However if you choose to keep your code as is, then take values of v that are much larger 20 or more to increase the jump frequency.Cheers! – PATCAT Jun 23 '14 at 6:32
You should consider embedding your comments directly into your answer. You can edit your answer by clicking "edit" at the bottom of it. Just an idea :) – Patrick Coulombe Jun 23 '14 at 6:41

Your procedure is correct. I just check in Monte Carlo Methods in Financial Engineering. In this book they use theta = 0; sigma = 0.4 and v = 1 and 0.5 (subordinator). With v = 1, you will get more peaked curve (fatter tails). As you reduce v, your pdf will looks like Normal.

To get the plot in Matlab.

S = price vector

You will get disjoint points (not line). If you find a better way to plot, please let me know.

Once you get the price vector, plot the PDF: S is a vector

 >mu = mean(S);
 > sigma = std(S);
 > x=linspace(mu-4*sigma, mu+4*sigma);
 > plot(x,normpdf(x,mu,sigma))
share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.