Re: [Quantlib-dev] CAT Bond valuation

[Luigi B. <lui...@gm...>]

Hi Grzegorz,
    as usual, apologies for the delay.

I've been looking at the RiskyBond class---I didn't remember it---and
I'm not sure of its approach. It tries to model bonds that can
default, but that's simply all bonds; it's just more or less likely
(and in fact, even when just discounting the amounts, one rarely uses
the risk-free curve; usually there's a spread added to the curve that
somewhat takes into account the possibility of default as an increased
discount factor that decreases the present value of the cash flows).

For modeling default explicitly, I wouldn't use a different class; I'd
just keep the existing one and, instead of a pricing engine that just
discounts, I'd use a pricing engine that takes default probability
into account in order to weigh the cash flow amounts. This way, the
same bond instance could be priced either way.

However, the above applies to the usual kind of bonds, in which a
coupon might disappear if the bond defaults but is otherwise fixed. In
your case, the coupon survives but varies in notional and amount,
which probably makes it a different beast, and the approach in
RiskyBond might work.  You could calculate your expected cash flows
based on your model (as RiskyBond does in expectedCashflows) and pass
those to the BondFunctions class for yield calculation etc.  Of course
this sidesteps the issues you found (such as amount() returning the
risk-free amount) but I think it can get you started quicker.

Later,
    Luigi


On Fri, Jan 4, 2013 at 5:33 PM, Grześ Andruszkiewicz <gan...@gm...> wrote:
> Hi,
>
> Coming back to the risky bonds, I am still trying to figure out what would
> be the best design. Obviously I know a few not-so-elegant ways to just make
> it work, so this is not what I am after.
>
> The first and maybe main question is what do CashFlow::amount() and
> Coupon::nominal() represent. By looking at Luigi's QL book, and the Bond
> class implementation, I would say that amount() is the expected amount of
> the coupon (this is implied by the implementation of NPV calculation for
> bonds), and nominal() is the risk-free nominal value (implied by the
> calculation of the capital repayments in the Bond class again).
>
> All this makes sense for risk-free coupons, but not really for the risky
> ones. To make the current NPV calculation work, we should assume that
> amount() returns the expected amount as I said, but this breaks the yield
> calculation. The yield in the risky case is usually used to compare the
> market-implied riskiness of two different bonds, because obviously comparing
> just the market price is not enough. Hence one should use the risk-free
> amount() for this calculation. As for the nominal(), one could safely use
> the risk-free value, but it might be inconsistent with amount() for notes
> where the notional changes (decreases) as e.g. defaults or catastrophes
> happen.
>
> Also I am not sure about what things like the clean and dirty price mean for
> a risky bond.
>
> A few immediate ideas:
> (1) Add a new virtual method to CashFlow for the riskfreeAmount() (a better
> name anyone?) with default implementation to return the amount(). Then we
> could change the Bond class to use the new value for appropriate quantities
> (yield() for example). This seems the cleanest way to do it, but it is a
> fundamental change in some core classes.
>
> (2) Create a base class for risky bonds, that inherits from the Bond class.
> Inside keep two copies of the the coupon list (or dynamically calculate one
> of these from the other)---one with expected amount(), and one with
> risk-free amount(). Override appropriate methods (yield() again for example)
> accordingly. This introduces obvious data and partly code duplication, but
> leaves the core classes unchanged.
>
> (3) Just go the same way as RiskyBond and subclasses (from
> experimental/credit) went---forget about the Bond subclass and use the
> amount() for risk-free values.  This is maybe the most pragmatic approach,
> but then some bonds are not a Bond... And we get loads of code duplication.
>
> I would be grateful for all comments and suggestions.
>
> Cheers,
> Grzegorz
>
> PS. What is the process for committing changes to the code base? Should I
> just commit using my Sourceforge account, or do I need extra permission? Are
> the changes reviewed by anyone?
>
>
> On 19 December 2012 15:18, Grześ Andruszkiewicz <gan...@gm...> wrote:
>>
>> Hi Luigi,
>>
>> After spending way too much time on reading termsheets and talking to
>> people I am finally ready to write some code :)
>>
>> I managed to find a class that seems rather similar to what I am trying to
>> achieve: RiskyFloatingBond in experimental/credit. It seems to create
>> coupons as if there was no credit (CAT in my case) risk. The risk is only
>> taken into account while calculating (1) NPV (2) expectedCashflows(). In my
>> case I would still need to run Monte Carlo simulation in these two places.
>> If I ignore (2) for now, then I hopefully will be able to use the standard
>> approach for MC.
>>
>> Have you seen this class before? It was written by Roland Lichters in
>> 2008. Unfortunately a quick search didn't find any associated tests. Is it
>> actually used?
>>
>> This kind of approach gives me an easy way to calculate the yield of the
>> bond (disregarding the risks), which is often used by practitioners to
>> compare different bonds, combined with expected loss.
>>
>> Kind regards,
>> Grzegorz
>>
>>
>>
>> On 15 October 2012 15:11, Luigi Ballabio <lui...@gm...> wrote:
>>>
>>> Grześ,
>>>     apologies for the delay.  As I was telling you, there's currently
>>> no example for coupon amounts calculated in a MC simulation.  If you
>>> want to go that route, you'll have to:
>>>
>>> - write the simulation itself.  There are a number of engines you can
>>> use as an example, so you should be covered with regards to creating a
>>> path generator, a path pricer and the several other pieces you'll
>>> need.  The notable difference in your case is that you'll want to
>>> return a number of cashflow amounts from the simulation, not a single
>>> number.  To do that, you'll have to use the second template argument
>>> of PathPricer: I think all the existing engines use its default (that
>>> is, Real for a single number) but you'll have to specify that you'll
>>> return a vector<Real> or something like it.
>>>
>>> - link the coupons to the simulation.  Again, there's no code doing
>>> this yet.  What I'd do is to create a new class inheriting from
>>> CashFlow and taking a pointer to the MC simulation.  When their
>>> amount() method is called, instances of this class should ask the
>>> simulation for the corresponding result.  In turn, this means that a)
>>> they should know which cashflow they are (the 1st, the 2nd...) among
>>> those calculated by the simulation and b) the simulation must
>>> implement some kind of caching to avoid being run several times as the
>>> Bond class asks its cashflows for their amounts.
>>>
>>> The above should keep you busy for a while :)
>>> Let me know when you need further advice...
>>>
>>> Later,
>>>     Luigi
>>>
>>>
>>> On Thu, Sep 13, 2012 at 5:56 PM, Grześ Andruszkiewicz
>>> <gan...@gm...> wrote:
>>> > Hi Luigi,
>>> >
>>> > Thanks for a long reply. We were just trying to follow your advice and
>>> > extend the Bond class, but we found a few potential issues:
>>> > 1. The Coupon class seems to have a fixed notional, whereas in our
>>> > case the notional could become smaller as a result of CAT events (that
>>> > deplete the notional of the CAT bond)
>>> > 2. The Bond class seems to assume that we can always calculate the
>>> > coupon amounts (independently for every coupon). I am not sure that
>>> > this is possible for CAT bonds (i.e. that coupons will be correlated
>>> > as a result of depleting the notional, catastrophe seasonality, etc.),
>>> > at least I am not comfortable to assume it at this point.
>>> > 3. Moreover, we wanted to have a way to price these instruments using
>>> > Monte Carlo techniques, i.e. use the underlying CAT engine to generate
>>> > random scenarios of events, given the events calculate the NPV of the
>>> > bond for every case, and average the results at the end. It is not
>>> > clear to how to achieve this with the Bond class...
>>> >
>>> > Are there other types of instruments in QuantLib with similar
>>> > characteristics, that we could use as examples?
>>> >
>>> > Kind regards,
>>> > Grzegorz
>>> >
>>> > On 31 August 2012 15:45, Luigi Ballabio <lui...@gm...>
>>> > wrote:
>>> >> Hi Grześ,
>>> >>     I'd start by doing the least possible coding :)   Let me
>>> >> elaborate.
>>> >>
>>> >> In the architecture of QuantLib, you'll need an instrument class
>>> >> (describing the contract) and an engine class (doing the actual
>>> >> pricing).  You can ask your resident expert (hi, Lorenzo) or read
>>> >> chapter 2 of <https://sites.google.com/site/luigiballabio/>.
>>> >>
>>> >> As for the instrument, it is very tempting to inherit it from the
>>> >> existing Bond class (it's a bond, after all).  In the short term,
>>> >> that's what I advice.
>>> >>
>>> >> In the long term, I'm a bit worried that functions taking a Bond
>>> >> instance (such as, for instance, BondFunctions::yield, which
>>> >> calculates the bond yield) would take a CAT bond and do their job like
>>> >> they do for each other bond; that is, extract its coupons and perform
>>> >> the yield calculations disregarding the catastrophe feature.  This
>>> >> might or might not be what you want.
>>> >>
>>> >> In the _very_ short term, though, I'd just use the existing fixed-rate
>>> >> and floating-rate bond classes and use those until you see that the
>>> >> thing works.  It will save you some development time which I'd rather
>>> >> use for getting to a first working version.
>>> >>
>>> >> Which brings me to the second part, i.e., the engine class.  It will
>>> >> probably need to contain a discount curve and your loss distribution.
>>> >> Any idea about how you'll use them?
>>> >>
>>> >> Later,
>>> >>     Luigi
>>> >>
>>> >>
>>> >> On Fri, Aug 24, 2012 at 5:08 PM, Grześ Andruszkiewicz
>>> >> <gan...@gm...> wrote:
>>> >>> Hi Luigi,
>>> >>>
>>> >>> Thanks for your reply! I personally can't claim to be proficient with
>>> >>> Quantlib, but my colleague Lorenzo (CC'd) did the 3-day course in
>>> >>> London with yourself, so he must be an expert ;)
>>> >>>
>>> >>> I don't think there are any established models for CAT bonds. We are
>>> >>> actually part of one of these academic-industry projects and one of
>>> >>> the goals is to come up with a model and implementation for these
>>> >>> instruments. We thought it might be a good idea to make this
>>> >>> implementation part of quantlib, to make it potentially useful for
>>> >>> someone.
>>> >>>
>>> >>> To start with, I would be grateful for any hints on where to start,
>>> >>> e.g. what would be your first guess on the place in the class
>>> >>> hierarchy where this instrument would fit?
>>
>>
>