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by czar3k
December 22nd, 2017, 6:21 pm
Forum: Student Forum
Topic: Variance Gamma Scaled Self Decomposable process (VGSSD model)
Replies: 22
Views: 10014

Re: Variance Gamma Scaled Self Decomposable process (VGSSD model)

In the meantime I found a more efficient version of matlab code that actually performs inverse Fourier transform on a given function. Article is  here It has some tunable options which I played around with and the results have definetely improved, but the procedure fails for some sets of VGSSD param...
by czar3k
December 22nd, 2017, 6:00 pm
Forum: Student Forum
Topic: Variance Gamma Scaled Self Decomposable process (VGSSD model)
Replies: 22
Views: 10014

Re: Variance Gamma Scaled Self Decomposable process (VGSSD model)

Yes, I did, but I have no idea what exactly should be done.
I guess it's about transformation of the integrand function in order to remove the undesired property (Dirac mass) so the integral becomes "numerically processable", Could you provide any example?
by czar3k
December 22nd, 2017, 12:02 pm
Forum: Student Forum
Topic: Variance Gamma Scaled Self Decomposable process (VGSSD model)
Replies: 22
Views: 10014

Re: Variance Gamma Scaled Self Decomposable process (VGSSD model)

What exactly is the regularization process about?
I assume it should help to get rid of numerical instability (at least in some cases), so I  guess it's worth trying.
by czar3k
December 20th, 2017, 11:20 am
Forum: Student Forum
Topic: Variance Gamma Scaled Self Decomposable process (VGSSD model)
Replies: 22
Views: 10014

Re: Variance Gamma Scaled Self Decomposable process (VGSSD model)

Well, not quite. If X(t) is the mathematical VGSSD process, then [$]\phi_{X(t+1) - X(t)}(u)[$] is the ratio of the expression on the r.h.s of (15) of O'Sullivan at t+1 and t. Then, for the risk-neutral stock price process, which has a compensator drift, you need something like (**) [$]f_{t,t+1}(u) ...
by czar3k
December 15th, 2017, 3:55 pm
Forum: Student Forum
Topic: Variance Gamma Scaled Self Decomposable process (VGSSD model)
Replies: 22
Views: 10014

Re: Variance Gamma Scaled Self Decomposable process (VGSSD model)

In that case what would be the expression for pdf of log(S(t+1)/S(t)) for any t in terms of VGSSD characteristic function? Below if the code for pricing options in VG model, it's ok, I checked it. I guess the right characteristic function for VGSSD would be: CF_VG = @(u)(1./(1-1i.*u.*theta.*nu.* sqr...
by czar3k
December 14th, 2017, 10:33 pm
Forum: Student Forum
Topic: Variance Gamma Scaled Self Decomposable process (VGSSD model)
Replies: 22
Views: 10014

Re: Variance Gamma Scaled Self Decomposable process (VGSSD model)

My goal is to simulate VGSSD process at least approximately there is no issue with VG. Maybe I misunderstand VGSSD process. I think that it is impossible to have everything at once: 1) distributions of daily returns from T(0)->T(1), T(1)->T(2), T(end-1)->T(end) are all skewed with the same skewness ...
by czar3k
December 12th, 2017, 11:03 pm
Forum: Student Forum
Topic: Variance Gamma Scaled Self Decomposable process (VGSSD model)
Replies: 22
Views: 10014

Re: Variance Gamma Scaled Self Decomposable process (VGSSD model)

Thanks for you 2 last post, they inspired me to "play around". As my math background is not strong enough to deeply feel and understand and rigourously follow your advise (those characteristic functions and numerical integration...) I decided to take different attitude. As I said I'm in a ...
by czar3k
December 7th, 2017, 10:50 pm
Forum: Student Forum
Topic: Variance Gamma Scaled Self Decomposable process (VGSSD model)
Replies: 22
Views: 10014

Re: Variance Gamma Scaled Self Decomposable process (VGSSD model)

Referring to your brute force simulation idea. Please let me know I understand correctly. If the characterictic function of a return of an asset at time t follows VGSSD dist and is expressed as (1-sqrt(-1) *sqrt(t)*nu*theta+0.5*t*nu*sigma^2)^(1/nu) then the characteristic function of dist. of return...
by czar3k
December 7th, 2017, 9:50 pm
Forum: Student Forum
Topic: Variance Gamma Scaled Self Decomposable process (VGSSD model)
Replies: 22
Views: 10014

Re: Variance Gamma Scaled Self Decomposable process (VGSSD model)

Thanks for your time on investigation! I think (just a feeling) that it is impossible that increments (daily returns) are at the same time: independent of previous increments , identically distributed and have a let's call it "kurtosis & skewness" preservation property - central limit ...
by czar3k
December 6th, 2017, 10:23 pm
Forum: Student Forum
Topic: Variance Gamma Scaled Self Decomposable process (VGSSD model)
Replies: 22
Views: 10014

Re: Variance Gamma Scaled Self Decomposable process (VGSSD model)

Thank you very much for your reply. Your remark concernign reversed N_sim & T is right, I was aware of that.   The code itself is correct, I verified it. Parameters are tuned to daily returns. I set them up as follows: drift = (theta + mu)*365 = 0.03 sigma*sqrt(365)  = 0.2 Running the code with ...
by czar3k
December 5th, 2017, 10:35 am
Forum: Student Forum
Topic: Variance Gamma Scaled Self Decomposable process (VGSSD model)
Replies: 22
Views: 10014

Variance Gamma Scaled Self Decomposable process (VGSSD model)

I’m using a Variance Gamma model to price some options with Monte Carlo method. My model is calibrated to daily returns data. There is no issue with this model as long as options are not path-dependent. For european options  I can simulate prices of a stock only at maturity (say 90 days) by simply s...