Merton76Process
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Hi,
I was wondering why the Merton76Process does not really adhere to the StochasticProcess interface. I do see that there is more to this process than a drift and a diffusion. The fact, however, that the drift and diffusion methods for the Merton76Process are implemented via QL_FAIL, makes it impossible to use this process in the way, a stochastic process is supposed to be dealt with. Would it make sense to incorporate the jump part into the diffusion method? The diffusion would be a random variable then but at least the interface of StochasticProcess would be satisfied. Alternatively, one might consider to break the inheritance and to build up the Merton76Process separately. If it does not behave like a normal StochasticProcess, why should it be one? Comments and thoughts on this welcome, wpe |
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Hello,
Lots of interesting financial models, such as variance gamma and normal inverse gamma, are pure jump models, so any redesign should take them into consideration. Bringing in a LevyProcess class, with drift, diffusion and jump methods might tidy things up. However, that is quite a large change and might cause more problems than it solves. Neil --------------------------------------------------- Neil Firth Brasenose College Oxford OX1 4AJ United Kingdom Office: 01865 280616 [hidden email] http://www.maths.ox.ac.uk/~firth --------------------------------------------------- |
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In reply to this post by Penschke, Walter
Neil,
Are you doing any work on Heston sto. vol.
and PIDE (not 100,000 miles (km)) away from current topic?
Cheers
Daniel
From: [hidden email] on behalf of Neil P Firth Sent: Mon 13/09/2004 18:11 To: Penschke, Walter Cc: [hidden email] Subject: Re: [Quantlib-users] Merton76Process Hello, |
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Daniel,
No, I'm not looking at stochastic volatility. I have had a brief look at the PIDE formulations for American option pricing on jump processes, but I'm not working on that directly either! Best Regards, Neil --------------------------------------------------- Neil Firth Brasenose College Oxford OX1 4AJ United Kingdom [hidden email] http://www.maths.ox.ac.uk/~firth --------------------------------------------------- On Mon, 13 Sep 2004, Daniel J. Duffy wrote: > Neil, > Are you doing any work on Heston sto. vol. and PIDE (not 100,000 miles (km)) away from current topic? > > Cheers > > Daniel > > > ________________________________ > > From: [hidden email] on behalf of Neil P Firth > Sent: Mon 13/09/2004 18:11 > To: Penschke, Walter > Cc: [hidden email] > Subject: Re: [Quantlib-users] Merton76Process > > > > Hello, > > Lots of interesting financial models, such as variance gamma and normal > inverse gamma, are pure jump models, so any redesign should take them into > consideration. Bringing in a LevyProcess class, with drift, diffusion and > jump methods might tidy things up. However, that is quite a large > change and might cause more problems than it solves. > > Neil > > --------------------------------------------------- > Neil Firth > Brasenose College Oxford OX1 4AJ United Kingdom > Office: 01865 280616 > [hidden email] > http://www.maths.ox.ac.uk/~firth > --------------------------------------------------- > > > ------------------------------------------------------- > This SF.Net email is sponsored by: YOU BE THE JUDGE. Be one of 170 > Project Admins to receive an Apple iPod Mini FREE for your judgement on > who ports your project to Linux PPC the best. Sponsored by IBM. > Deadline: Sept. 13. Go here: http://sf.net/ppc_contest.php > _______________________________________________ > Quantlib-users mailing list > [hidden email] > https://lists.sourceforge.net/lists/listinfo/quantlib-users > > > |
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In reply to this post by Penschke, Walter
Hello,
I agree that the implied changes are considerable. And I definitely do not yet know all of QL! Having put the focus so far on MC-simulation, I'd say that primarily the PathGenerator would be involved. One idea would be to delegate (again) to the StochasticProcess. But then - in the case of a jump diffusion process - we also would need more than the currently available gaussian Rsg. Presumably a Poisson-Rsg also would be required. This again violates the current setup of the PathGenerator. I therefore thought about creating the PathGenerator not via a gaussian random sequence generator, but via a sequence generator factory (yet to do), who could also create other random number sequences, e.g.: from a poisson distribution. In the next() method of the PathGenerator this factory could be passed over to the StochasticProcess, which in turn could sample from (any kind of) distribution in order to simulate the process specific behaviour (e.g.: also jumps). As a consequence there would be the need for a new method within the StochasticProcess interface (sample()), which takes this factory and may be other parameters and samples according to its specific nature. Alternatively, I could envisage a second version of the PathGenerator class itself, which then knows how to evolve jump diffusion processes and queries these kind of processes accordingly. This does not seem to be too nice, because we would need an extra class. However, the existing stuff would not be affected. I am also not quite sure about the Path class (in MonteCarlo). Using jump diffusion processes with MonteCarlo possibly requires a third array inside Path, modelling the jumps. Alternatively the Path could only keep track of the values and does not care about the individual components (drift, diffusion, jump), which make up the values of the Path. Comments welcome. wpe -----Original Message----- From: Neil P Firth [mailto:[hidden email]] Sent: Monday, September 13, 2004 5:11 PM To: Penschke, Walter Cc: [hidden email] Subject: Re: [Quantlib-users] Merton76Process Hello, Lots of interesting financial models, such as variance gamma and normal inverse gamma, are pure jump models, so any redesign should take them into consideration. Bringing in a LevyProcess class, with drift, diffusion and jump methods might tidy things up. However, that is quite a large change and might cause more problems than it solves. Neil --------------------------------------------------- Neil Firth Brasenose College Oxford OX1 4AJ United Kingdom Office: 01865 280616 [hidden email] http://www.maths.ox.ac.uk/~firth --------------------------------------------------- |
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