Re: [Quantlib-dev] [Quantlib-users] Pricing Callable Capped Floaters within a HullWhite Tree

[Guowen H. <GH...@dt...>]

Please keep in mind
1. the call schedule does not have to match the coupon schedule, 
2. the quoted call price is kind of clean, and 
3. the simulated prices are always dirty price and the backward induction 
values on the tree are kind of dirty price (including accrued interest)

So, the call prices are not necessary the paid off price when the calls 
are exercised.

Guowen


 



"Toyin Akin" <toy...@ho...> 
Sent by: qua...@li...
07/19/2006 03:40 AM

To
lui...@gm...
cc
qua...@li..., qua...@li...
Subject
[Quantlib-users] Pricing Callable Capped Floaters within a      HullWhite 
Tree







Hi all,

I am looking at the possibility of pricing callable capped floater using 
QuantLib and it seems like most of the code to price such a product is 
more 
or less within Quantlib already (parts of the logic is present in 
different 
classes).

Basically I want to price, for each period, the following

Libor() - Caplet(Libor, X)*Notional*AccuralPeriod , callable @ $Y for each 

period.

This has to be priced via a tree methodology and the Libor() - Cap(Libor, 
X)*Notional*AccuralPeriod
part can be priced by

1) implementing the Libor() pricing via the float leg code that is part of 

the DiscretizedSwap class
2) implementing the Caplet(Libor, X) pricing via the cap leg code that is 
part of the DiscretizedCapFloor class

Thus these two legs can be pulled out to form a class like the 
DiscretizedSwaption class.

The issue I have is how to price the callable part.

Now I have this little description of the callable algorithm from the 
FinancialCAD web site :

###########################################################
The price of a callable capped floater is obtained by building a trinomial 

interest rate tree, constructing the yield curve on each node of the tree, 

and re-valuing the capped floater (note) on each node.  On nodes that are 
exercise dates, the price of the note is compared to the call and/or put 
price(s).  If it is possible for the issuer to call, and the call price is 

less than the note price, then the call option is exercised and the price 
of 
the option on that node is the difference between the call price and the 
note price.  If the note is not called and it is possible for the holder 
to 
put, and the put price is greater than the note price, then the put option 

is exercised and the price of the option on that node is the difference 
between the put price and the note price.  The option price is rolled back 

to earlier nodes on the tree and re-calculated as above depending on 
whether 
or not the option is exercised.  The option price rolled back to the value 

date is added to the price of the non-callable capped floater on the value 

date to get the price of the callable capped floater.
###########################################################

My question is regarding the statement " difference between the call price 

and the note price".

Again the note can be computed easily via the "Libor() - Caplet(Libor, 
X)*Notional*AccuralPeriod" expression. The note is priced backwards in 
time 
and each time you step back, an extra coupon period is added onto the note 

(at each node).

The tree that quantlib builds for interest rate pricing (ie - capfloor via 

tree) assumes that you are standing on the start date of a coupon period 
(see preAdjustValuesImpl() of the DiscretizedCapFloor() class). Thus you 
cannot use the regular max(L-X,0) expression to value a cap, but a 
modified 
version to take into account that you are standing on the start date of a 
rate fixing and not the end.

Thus, FINALLY!!, the question I am asking : Is there an adjustment that 
one 
needs to perform on this "difference between the call price and the note 
price" because we are standing on the start date of each coupon period.

I am making the assumption that the $Y callable price is to be paid at the 

each of each callable period. Is this the normal convention?

Long winded I know...!!
Toy out.



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