I got a great response to my maths sweet spot blog. Great in the sense of numbers of people writing to me and great in the sense that every single one of them agreed with me!
But it’s still going to be years before the tendency for people to make quantitative finance as difficult as they possibly can is eradicated. And that’ll be years while money is lost because of lack of transparency and lack of robustness in pricing and risk-management models. (But on the other hand, there’ll be lots of research papers. So not all bad news then!)
There’ve been a couple of recent forum threads that perfectly illustrate this unnecessary complexity. One thread was a brainteaser and the other on numerical methods.
The brainteaser concerned a random walk and the probability of hitting a boundary. Several methods were proposed for solving this problem involving Girsanov, Doleans-Dade martingales, and optimal stopping. It must have been a really difficult problem to need all that heavyweight machinery, no? Well, no, actually. The problem they were trying to solve was a linear, homogeneous, second-order, constant-coefficient, ordinary differential equation! (Really only first order because there weren’t even any non-derivative terms!) The problem was utterly trivial (although, if you look at the thread, I did still manage to make a sign error, typical!). Talk about sledgehammers and nuts.
The other thread was on using non-recombining trees to price a simple vanilla option. People were really helpful to the person asking for advice on this topic. But no one, except for me, of course, asked the obvious question “Why on Earth are you doing such a silly thing?” I can hardly imagine a more cumbersome, slow, and generally insane way to solve a simple problem.
It disturbs me when people have been educated to such a level of complexity that they can throw about references to obscure theorems while at the same time being unable to think for themselves. To me, mathematics is about creativity in the use of tools not about being able to quote ‘results.’ Even knowledge of the names of mathematicians and what they are famous for is something I find a bit suspect. If you know the names of all the theorems but don’t know when to use them then you are an historian not a mathematician. Perhaps maths is an art, and I’m not impressed with painting by numbers.