Inflation Questions (repeated)

[Peter Caspers-4]

Hi,

    since currently there seem to be a few people active in the
inflation part of the library, may I resend the question below ( I
hope I did not get an answer, at least I do not remember ) ?

Thanks
Peter


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 <[hidden email]>
Date: 2012/12/17
Subject: Inflation Index Interpolation
To: [hidden email]


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

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