[Quantlib-dev] Fwd: Inflation Index Interpolation / yoy volatility structure

[Peter C. <pca...@gm...>]

Hi,

just as an update to the point below: The second way of interpolating seems
to be the correct one. I do not have a suggestion for a fix in ql however
(as I said below, everything under the assumption that my understanding of
the intended usage of the classes is correct).

I have a second question on inflation in ql concerning the yoy volatility
structure. I am trying to use a KInterpolatedYoyOptionletVolatilitySurface.
Retrieving a volatility for say maturity = 1y and a strike k the following
happens:

1 YoYOptionletVolatilitySurface::volatility( today + 1y , k ) is called.
The observation lag (3m) is subtracted from the maturity date and the time
to reference date is computed giving (apprx.) t  = 0.75. Then
volatilityImpl(t,k) is called =>

2 KInterpolatedYoYOptionletVolatilitySurface::volatilityImpl(t,k)
recomputes a physical date d from t=0.75 giving something like d =
today+9m and then retrieves a volatility slice for this d from the
yoyOptionletStripper, which is in my case an
InterpolatedYoYOptionletStripper =>

3 InterpolatedYoYOptionletStripper::slice(d) computes for each relevant
strike k a volatility by invoking volatility(d,k) on the respective
volatility curve. The latter is a PiecewiseYoYOptionletVolatilityCurve.
This triggers executiion of

4 YoYOptionletVolatilitySurface::volatility( today +9m , k ) which we
already had above. Again the observation lag (3m) is subtracted and we
arrive at today + 6m and (apprx.) t = 0.5, which is used as input to

5 InterpolatedYoYOptionletVolatilityCurve::volatilityImpl(t) which finally
returns the volatility for t=0.5.

It should be t=0.75 in my opinion however. I do not have a general fix, but
only a workaround changing the call in 2 into

slice_ = yoyOptionletStripper_->slice(d + this->observationLag() );

which should work if the default observation lag is used in 1.

Is my observation correct and would you consider the workaround more or
less reasonable ?

Thanks a lot for any input
Peter

---------- Forwarded message ----------
From: Peter Caspers <pca...@gm...>
Date: 2012/12/17
Subject: Inflation Index Interpolation
To: qua...@li...


Hi,

I am comparing Murex and QuantLib concerning Inflation Pricing. I observe a
difference in the way an index fixing is interpolated between known (i.e.
already fixed) values. Here is an example:

Take the EUHICP XT index which has fixings

01.08.2012 (Aug 12)    115.10
01.09.2012 (Sep 12)    115.97

Now I want to look up the fixing on 28.08.2012 belonging to an observation
date on 28.11.2012 (3m observation lag). In QL the interpolation is done as
follows:

Days between 01.08. and 01.09. = 31, Days between 01.08. and 28.08. = 27,
Interpolated Fixing = 115.10 + 27/31 * ( 115.97 - 115.10 )

In Murex on the opposite:

 Days between 01.11. and 01.12. = 30, Days between 01.11. and 28.11. = 27,
Interpolated Fixing = 115.10 + 27/30 * ( 115.97 - 115.10 )

Which computation is the correct one, i.e. what is the market convention
that is actually applied to deals ? Maybe I am using the QL classes not as
intended ?

Thanks a lot
Peter