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boostraping a YC in the past

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DU VIGNAUD DE VILLEFORT FRANCOIS GASAPRD PHI

boostraping a YC in the past

Hi all,

I try to boostrap a YC in the past (to compute a some historical correlation matrix). Ideally I would like to change the evaluation date and use the index historical values stored in the corresponding time serie. Yet I have the impression that if one changes the evaluation date YC are bootstraped as of this date using the values provided by the quotes (instead of the historic fixings). Any idea ?

François

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Ferdinando M. Ametrano-3

Re: boostraping a YC in the past

Hi François

my suggestion is:

loop currentDate backward from the latest date to the earliest one
get fixings from Indexes and set them to your relevant Quotes
set the EvaluationDate equal to currentDate
(re-)build RateHelpers and YieldCurve
calculate forward rates at constant interval (e.g. 6M), not constant dates
calculate fwd rate differences, and add them to a SequenceStatistics class
get correlation from SequenceStatistics

investigate more sophisticated alternatives only when this very basic
approach is working...

ciao -- (your current manager :-) Nando

On 5/31/07, DU VIGNAUD DE VILLEFORT FRANCOIS GASAPRD PHI
<[hidden email]> wrote:

>
>
>
>
> Hi all,
>
>
>
>
>
> I try to boostrap a YC in the past (to compute a some historical correlation
> matrix). Ideally I would like to change the evaluation date and use the
> index historical values stored in the corresponding time serie. Yet I have
> the impression that if one changes the evaluation date YC are bootstraped as
> of this date using the values provided by the quotes (instead of the
> historic fixings). Any idea ?
>
> François
> -------------------------------------------------------------------------
> This SF.net email is sponsored by DB2 Express
> Download DB2 Express C - the FREE version of DB2 express and take
> control of your XML. No limits. Just data. Click to get it now.
> http://sourceforge.net/powerbar/db2/
> _______________________________________________
> QuantLib-dev mailing list
> [hidden email]
> https://lists.sourceforge.net/lists/listinfo/quantlib-dev
>
>

Bianchetti Marco

Re: boostraping a YC in the past

In reply to this post by DU VIGNAUD DE VILLEFORT FRANCOIS GASAPRD PHI

Concerning the following version for the calcualtion of historical
correlations on forward rates to be used in the Market Model:

> loop currentDate backward from the latest date to the earliest one
> get fixings from Indexes and set them to your relevant Quotes
> set the EvaluationDate equal to currentDate
> (re-)build RateHelpers and YieldCurve
> calculate forward rates at constant interval (e.g. 6M), not constant
dates

This last point is controversial.
For LMM we need a correlation matrix among forward rates of kind
L(t,S,T), observed at t<S, between dates S<T.

1) So for each past date t'<t-D one would calculate the forward rate
between the *same* dates L(t',S,T), the only difference being the
observation time.

Instead:

2) Calculating the forward rates in the past at constant interval
L(t',S',T') with S'=S-D and T'=T-D amounts to calculate *different*
forward rates, so the financial meaning is poorer in my opinion.

This is also consistent with the discussion given in Brigo & Mercurio,
2nd edition, par. 6.19.1.

Any other opinion ?
Well, probably the best thing to do at the end is to implement both
methods (not much extra work) and go for testing on the market...

Ciao
Marco

> calculate fwd rate differences, and add them to a SequenceStatistics
class
> get correlation from SequenceStatistics

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