March 14th, 2005, 1:27 pm
Hi Emmy, I wouldn't give up just yet, but be warned it isn't gonna be easy. You can look at the thread 'Finite difference - CFD technique' on the software forum to see my background but you can see that I came from CFD as well. I would recommend to you to forget about the Black-Scholes PDE for the moment and really go back to basics. As an ex CFD person, I find it is always tempting to just go ahead and write code to solve the BS pde as a convection-diffusion equation and think that is the be all and end all of things. You need to understand where the BS pde comes from and to do that you need to forget about it for a while. Firstly, you need to make sure you have all your basics covered. Go and get some revision guides/and or text books at an undergrad level ( in my case I needed to look at some high school books as well !! ) and go through the exercises making sure you can calculate expectations, integrate/differentiate, find limits of series, taylor series etc. If you can already do them then great, but for me I found I had to painstakingly go through the exercises in these books until I actually understood and could use these mathematical techniques. Also, doing exercises is far more beneficial than just reading, as a) you understand things better and b) you can actually apply them, for example, in an interview. Secondly, get Hull or Neftci and start going though the exercises in these. Both have solutions manuals and you can check your working. You need to understand what is meant by a risk-neutral probability, a martingale, filtrations, girsanov theorem etc. Usually tree models such as CRR are used to illustrate how options are priced using martingales or binomial replication, so you get some practice building trees. You can practice coding some tree models to improve your coding skills. Once you start shifting from discrete probability distributions to continuous ones then you'll also get more practice in solving SDE's and this is also probably a good point to practice coding Monte Carlo techniques as you can relate the analytic solution of your equations to the numerical solution. Eventually you'll see how all of these methods relate to PDE's. After this there are a wealth of books such as Oksendal or Karatzas and Shreve, which really go into the real depths of stochastic calculus, and hopefully after doing the above you should have a grounding to attempt this tougher stuff. You can also started looking at some of the more advanced options pricing techniques such as stochastic or local volatility models. Unfortunately, this is not a linear process and sometimes you do feel like you are just hitting your head against a wall with this stuff, but trust me if you keep at it, it will make sense. With your qualifications + the finance + your CFD knowledge, should mean you'll be able land a quant job in no time. Blade