Posted by
luca ferraro-2 on
Oct 07, 2008; 4:06pm
URL: http://quantlib.414.s1.nabble.com/Re-Error-irregular-fixings-not-yet-supported-in-LMM-calibration-with-CapHelpers-tp6899.html
Klaus Spanderen <klaus <at> spanderen.de> writes:
> Reference date of the term structure used to instantiate the
> calibraton helper and the index should be
>
> index->fixingCalendar().advance(todaysDate, index->fixingDays(),
> Days);
>
> I guess the best way to fix it is to roll your bootstrapped curve
> forward by index->fixingDays()
Klaus, many thanks for your answers.
Anyway, I have many doubts and questions about how to set up QL LMM
calibration, since very little documentation is available. I already
know nobody would answer this kind of post :-) I'm going to attend
Mark's course, but I wish to be already able to do the basics.
Let's start with an example:
Suppose I want to price a 1x4 vanilla european swaption (1Y frequency
for the fixed leg, 6M for the floating EURIBOR 6M index) ... we need to
evolve the forward rates F(t;T_{i-1},T_{i}), where T={1Y6M, ... , 5Y},
up to time t=T_{1Y}.
What I would do in QuantLib is to choose a Volatility and Corr model and
build a LFM process of size 8, bound to a EURIBOR 6M tenor index. Right?
(Any method or class to reduce rank size of the process?)
Questions on calibration with QL:
Now I need 8 instantaneous volatilities \sigma_{T_i} to be calibrated,
using at least 8 caplet vols, related to the following atm caplets:
Caplet1(T_{1Y},T_{1Y6M}) , Caplet2(T_{1Y6M}, T_{2Y}), ... ,
Caplet8(T_{4Y6M}, T_{5Y}). Market provides me 1 year tenor ATM CAPs vols.
1) Which CapHelpers do QL need? I would provide market quoted ATM CAPS
starting from 2Y tenor up to 5 years, is it enough/correct in current QL
LMM framework?
2) Do I have to provide CAPS with the same tenor of the underlying LMM
index? (ATM CAPS quotes are tipically 1Y based, while in my example I
use a EURIBOR 6M index for the LMM process).
3) What if I have "holes" between available market atm caps quotes
(tipically between 10Y and 30Y): how do I extrapolate atm cap vol from
market data?
I really hope someone would answer or at least point me to the right
direction. An example of a LMM calibration with real market data to
price a vanilla swaption would be really appreciated!
Best regards,
luca
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