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

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Hey Guowen,

Thanks for the tip.
The dirty pricing bit is a big help for structures whose start date is in 
the past.

I actually forgot about the fact that you can call on ANY date. However I 
assume that coupon dates are the most commonly dates that are chosen for 
calling any structure.

Thanks again,
Toy out...

>From: Guowen Han <GH...@dt...>
>To: "Toyin Akin" <toy...@ho...>
>CC: 
>qua...@li...,qua...@li..., 
>lui...@gm...,qua...@li...
>Subject: Re: [Quantlib-users] Pricing Callable Capped Floaters within 
>a	HullWhite Tree
>Date: Wed, 19 Jul 2006 09:07:08 -0400
>
>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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