Posted by
quantlib-users-admin on
URL: http://quantlib.414.s1.nabble.com/Libor-Forward-Process-tp4723p4731.html
> Hi Fabio,
>
> in general the starting dates and the day counting etc. is chosen to be=
> (hopefully;-) "compatible" with the existing cap/floor pricing to ensu=
re
> that the LMM cap/floor prices match to the prices of the BlackCapFloorE=
ngine
> in blackcapfloorengine.hpp or test-suite/capfloor.cpp
>
> You wrote:
> > 1) In the market cap volatility matrices, usually the first quoted ca=
p is
> > referred to the rate which fixes today and has accrual start date 2
> > business days after today, is it right? If so, in order to have a coh=
erent
> > structure for the forward rates to be used in LMM, the first fixing d=
ate
> > should be today (or the term structure reference date) and the first
> > accrual start date 2 business days after.
> agree.
> > In lfmprocess.cpp (line 49 and following), on the contrary, it seems =
that
> > today is the first accrual start date (the settlement) and the first =
fixing
> > date is 2 days before.
> The reference date of the index term structure is the settlement date, =
which
> is usually today+2 business days (line 49, the term structure is assume=
d to
> be spot, meaning today+2 business days, see also e.g. test-suite/
> capfloor.cpp, routine setup()). startDate of first fixing date is today=
(line
> 50). The first accrual start date is again usually the settlement date =
(line
> 69).
>
> > 2) in lfmprocess.cpp, lines 49-70, where the times vector are filled,=
the
> > accrual start and accrual end times are evaluated starting from the
> > settlement date, while the fixing times from the startDate, which is =
n days
> > before settlement. Could you please explain why the reference date is=
not
> > the same for all the vectors?
> The times vector are intend to be compatible to them in ql/Instrument/
> capfloor.cpp (startTimes_, endTimes_ and fixingTimes_) to ensure consis=
tent
> pricing. Shortly spoken the accrual times are related to the term struc=
ture
> therefore they are evaluated using the term structure reference date, w=
hich
> is the settlement date. The fixing times are used to determ the volatil=
ity of
> the caplets. Therefore they are evaluated from startDate. (see also
> blackcapfloorengine.cpp)
>
> > 3) the day counter used to calculate the times vectors in lfmprocess.=
cpp
> > seems to be the index day counter (see line 44), but, to remain coher=
ent
> > with all the other QuantLib instruments, it wouldn\'t be better to us=
e the
> > term structure day counter instead?
> The initial values of the LMM libor rates are taken from the indexed co=
upons,
> which are using the method indexFixing() from the index object. Therefo=
re the
> initial rates are calculated using the day counter of the index (s.
> xibor.cpp, line 108). To be consistent and to make Monte Carlo pricing =
easier
> we are IMO better off using the index day counter for the times vectors=
.
> Please notice that accrualStartTimes and accrualEndTimes aren't used
> internally by the LiborForwardModelProcess. They are just calculated fo=
r
> convenience reasons to make life for MC pricing easier, s. test-suite/
> libormarketmodelprocess.cpp. (It is safe to use different day counters =
for
> the term structure within the index or for the volatility term structur=
e
> within the LfmHullWhitePrameterization etc.)
>
> hope that this helps and please comment on inconsistencies.
>
> cheers
> Klaus
>
>
>
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