The horizon of financial planing and development has been dramatically changing through development and continuous up-gradation of a relatively new discipline known as Mathematical Finance. It is a branch of mathematics which enjoys relatively high degree of real life application compare to other traditional branches of mathematics.
It’s not long back when Mathematics had been used mostly as a language of physical sciences alone. Development and continuous contribution of researchers to enrich the branch of mathematics known as stochastic calculus, open a far greater opportunity for mathematicians to work as business analyst. Realizing the necessity of such technically sophisticated people in increasingly pro-business world, most of the renowned schools in the world responded urgently to cater the future demand of such a flourishing job market across the globe. However what is relatively missing is the back-ward linkage relevant programs in the elementary levels.
Who are under real focus? Is it students with Mathematics background or those with Finance background? It’s difficult to provide a straightforward answer. That’s because concentrations in both Mathematics and Finance are heterogeneous in different ranked schools over the world. If we talk about a North American Finance program, then the extent of mandatory quantitative courses in their program is no doubt substantial. On the other hand if we talk about ranked European institutes of business studies, the quantitative courses are mostly optional.
This forces European doctoral students in this area to struggle severely in maintaining a decent survival into the program. At the same time many ranked mathematics schools in the world have now blended quantitative finance courses into their graduate program and in many cases their students are highly valued in the job market where a demand for these technically sophisticated hands is apparently high. However the basic set-up of undergraduate course is clearly distinct from those of Mathematics or Finance requirements.
Experience suggests that all the mathematical finance, or actuarial mathematics, programs have first two years of intensive mathematics courses, with emphasis on elementary to sophisticated calculus and partial differential equation oriented courses parallel to those of abstract integration oriented measure theoretic courses (yielding a strong foundation on manipulating integrals in randomly evolved path space). Then the remaining two years are rightly been utilized to develop simulation oriented advanced courses used in particular in Mathematics of investment and stochastic process oriented courses.
A distinctive feature is that most of the courses in last two years are loaded with projects preparing the students to work with existing models in interest rate modeling, option and other derivative pricing and financial risk management. Advanced courses essentially involve not the differential and partial differential equations but the stochastic differential and stochastic partial differential equations. And to be honest there is hardly any way out to contribute in this arena without getting hands dirty with these advanced stuffs.
A good book for self-study is “A course in derivative securities: Introduction to theory and computation”. This book was published in 2005, written by Professor Kerry Back, a Mathematics oriented Finance faculty in business school at Texas A&M University. I assure the industry people not to get afraid of mathematics involved (though I do agree it’s not that easy), as I do highly appreciate his way of explaining mathematical intuitions with full set of computer codes. All the codes are encrypted in the body of the book and also can be easily downloaded from his web-site: www.kerryback.net. The codes are written in Visual Basic for excel users but can be easily recomposed in any other language like Mathlab, Mathematica. I again assure this book is written not only for academics but for academics and practitioners alike. Another book written by Professor Kevin Dowd is “Measuring Market Risk.” It’s a good reference in risk management through Europe and America. The codes for this book, written in mathlab, are rather involved and huge. Buying these books will no doubt give you immense pleasure in your late life when your wife’s closeness will no longer be as attractive as it used to be (very natural, isn’t it?).
Through these two books one can develop sound quantitative back-ground for analysing and planning financial trades. Of-course nothing is enough in this fascinating field and focus should be given which literature could give a working knowledge in short time to start with.