Re: [Quantlib-users] Hull-White and CIR path generation

[Simon Ibbotson-2]

Hi All,

I'm doing some work on path generation (Monte-Carlo) for the CIR
process.

I've written some code for generating random numbers for the Gamma
distribution, the Chi-squared distribution and the Non-Central
Chi-Squared distribution but I need to wrap these up into a path
generator for CIR which can then be used for Monte-Carlo pricing.

I can see some examples of random-sequence generators within the
MonteCarlo framework.
But I don't want to use the InverseCumulativeRsg as inverting the CIR
distribution is really slow compared to sampling from the Non-Central
Chi-Squared.

So, I'm assuming that (to use the Monte Carlo framework) I need to
create
1) A CIR sequence generator.
2) A RNG traits template class which enables the CIR sequence generator
class.

Is this correct? Or is there something that I've missed?

Thanks,

Simon



-----Original Message-----
From: Luigi Ballabio [mailto:[hidden email]]
Sent: 13 October 2010 15:34
To: Kamtsa Dragoslav
Cc: [hidden email]
Subject: Re: [Quantlib-users] Hull-White and CIR path generation

On Sat, 2010-10-02 at 12:49 +1000, Kamtsa Dragoslav wrote:
> I want to use the Hull White 1F and the CIR 1F implementations to
> generate explicit short rate/intensity paths. Could someone please
> point me to the relevant example or unit test to get me started,
> especially for the latter?

I'm afraid we're short on examples, but you might want to look in
<ql/processes>, especially hullwhiteprocess.hpp.  I don't remember
exactly what paths are generated if you plug the processes there in a
PathGenerator (short-rate, I guess, but I'm not certain) but at least it
might give you an idea on how to implement a CIR process (which, I'm
afraid, we don't have at this time.)

Luigi


--

When all else fails, pour a pint of Guinness in the gas tank,
advance the spark 20 degrees, cry "God Save the Queen!", and pull
the starter knob.
-- MG "Series MGA" Workshop Manual



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[Luigi Ballabio]

On Fri, 2010-10-15 at 16:50 +0100, Simon Ibbotson wrote:

> I've written some code for generating random numbers for the Gamma
> distribution, the Chi-squared distribution and the Non-Central
> Chi-Squared distribution but I need to wrap these up into a path
> generator for CIR which can then be used for Monte-Carlo pricing.
> [...] I don't want to use the InverseCumulativeRsg as inverting the
> CIR distribution is really slow compared to sampling from the
> Non-Central Chi-Squared.
>
> So, I'm assuming that (to use the Monte Carlo framework) I need to
> create
> 1) A CIR sequence generator.
> 2) A RNG traits template class which enables the CIR sequence generator
> class.
>
> Is this correct? Or is there something that I've missed?

Correct.  You can already generate numbers according to your
distribution, so just wrap them in a sequence generator and you should
be done.

Luigi


--

Better to have an approximate answer to the right question than a
precise answer to the wrong question.
-- John Tukey as quoted by John Chambers



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