[Quantlib-users] Re: lmm process

[Klaus S. <kla...@fr...>]

Enrico Michelotti wrote:

>1- Why th first forward is set to start at time zero and not at any time?
>If you have a general schedule not starting today? Do I need to interpolate 
>rates?

At the time being it is more important for me to get various volatility and 
correlation parameterizations working. Supporting non matching accrual 
periods should IMO be implemented after a "real" calibration of libor forward 
models is working. 

>2- The simulated forwards are very good (and also caplets) for maturities 
>shorter than 5y-8y. But if the mk caplet volatility is not well behaved (or 
>sufficiently smooth) the process crasches during the costruction of lambdas:
>In fact if vol2 = vol(i)*vol(i)*t(i) is smaller then vol1 = 
>vol(i-1)*vol(i-1)*t(i-1) then l = vol2- vol1 <0 and sqrt(l/delta(i-1)) 
>crashes. Dou you have any ideas? Do you think could be possible to use a 
>parametric version of caplet volatility?

The caplet volatility boostrapping is known to be "sensitive" if the caplet 
volatility is not sufficiently smooth;-(

In my current version the lmm process can be parameterized using different 
volatility and correlation models including the caplet volatility 
bootstrapping but also parametric versions are available. (see  e.g. 
http://www.exoticderivatives.com/Mas_papers.html). For the parametric 
versions we need the calibration facility working and that is what I'm 
currently working on (calibration helper stuff etc.). Hopefully I get this 
stuff ready before 0.3.12 is out.

>3- Why does the drift function take the deltas instead the accrual periods? I 
>think it should use the accrual period instead, due to the fact that: P(ti, 
>ti+1) = 1/(1+ delta(i)*Fi) and the delta should be the accrual period on 
>which the forward is built.

At the beginning I followed the Hull White article 
(www.rotman.utoronto.ca/~amackay/fin/libormktmodel2.pdf) where the deltas are 
defined as the time periods between the reset dates. I fixed this imprecision 
for the CapletLiborMarketModelProcess::discountBond method but I've missed 
the drift method.  For non-pathological situations one will hardly recognize 
the difference in a Monte-Carlo simulation. I ran some examples with millions 
of paths and didn't get differences bigger than the MC error. Thanks for the 
hint, I'll fix this with the next version. 

cheers
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Klaus Spanderen
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