Model Risk Seminar in Vienna

17-Jun-08, Vienna. Over 30 quants and risk experts joined Andreas Binder and Michael Aichinger on their tour through the most beautiful, but dangerous fields of mathematical finance. In the spirited discussion it turned out again that it is recognized that different models applied on the same deal type will usually lead to different prices (If they really differ, distrust the instrument)). Not so surprisingly, the surprise that good, but complex, model information can get lost in the numerical jungle and evaporate to ground-fog.

Next Model Risk event: 15-Jul-09, Zurich.

The UnRisk Language: Callable Bonds

UnRisk code: click to enlarge

Let's assume we want to price the following callable fixed rate bond:
- the underlying bond pays annual coupons of 5.2%, following the 30/360 day-count convention and corresponding to a nominal amount of 100,000 EUR
- the first coupon period starts at October 10, 2008 and the redemption (the nominal amount) is paid at October 10, 2018
- in addition, the bond is callable at each coupon date, starting from October 10, 2011

What are the steps to translate the termsheet of this callable fixed rate bond into the language of UnRisk?
The picture above gives the answer (due to the descriptive language of UnRisk, the code does not need to be explained in detail): First, the underlying fixed rate bond is constructed - this is done by the constructor MakeFixedRateBond. In the next line it is shown how the cashflows of the underlying bond may be generated (the function Cashflows is applied). In order to make the bond callable, a call schedule (constructed by MakeCallPutSchedule) has to be assigned - the callable bond is then constructed by the use of the function MakeCPFixedRateBond. That's about it.

The next question is: How do I get a fair price for this callable bond under, e.g. , a Hull & White (or a Black Karasinski or a LIBOR market) model?
Again, the picture above shows how this can be done: First, the Hull & White model has to constructed - we use the command MakeGeneralHullWhiteModel (usually this has to be done by the use of the UnRisk calibration routine, which identifies the parameters of the interest rate model from given bond, cap and swaption prices). The available interest rate models (especially their calibration) will be explained in a later blog.
But let's come back to our callable bond: By the use of the function Valuate (which may be used to price any financial instrument under any model) we gain the fair value of the callable bond under the given Hull & White model (the credit spread is assumed to be 80bp). The returned list contains the dirty / clean value of the underlying bond, the value of the call option and the dirty / clean value of the callable bond.

Symbols or Numbers?

I start this Blog label "Mathematics" with a reference to Paul Wilmott's Blog Numbers People and Symbols People. Paul named as one of the most influencing quantitative analysts, in his blog he discusses the ability of people to handle abstractions.

If UnRisk was a City Guide

It most probably was a Wallpaper . They present a tightly edited discreetly packaged list of the best a location has to offer the design conscious traveler. Wallpaper CG are compiled by the magazine's travel experts providing up-to-the-minute information.
Each guide combines info on Landmarks, Hotels, Urban Life, Shopping, Sport, Architours and Escapes. As a business traveler, I like the 24 hours, see-the-best-of-the-city-in-just-one-day, section. WCG issues are sub compact. I put it in a pocket of my jacket and it goes where I go.

Save Wallstreet's Soul?

Newsweek published the following article recently: Revenge of the Nerd  
Paul Wilmott is a 49-year-old Oxford-trained mathematician ond arguable the most influential quant of today .. Wilmott has cultivated a loyal following of truth-seeking converts from the failed school of thoughts that the entire world can be turned into Greek symbols, plugged into equations priced and predicted...