In the past decade, an increasing number of researchers from mathematics and physical sciences have been contributing together with their peers from economics and social sciences to the rapidly growing field of quantitative finance. This field, whose creation was marked by such important breakthroughs as the Modern Portfolio Theory of Markowitz, Capital Asset Pricing Model of Sharpe, Lintner, Mossin and Treynor, and Option Pricing Theory of Black, Scholes and Merton, has always relied on the power of mathematical tools and methods to discover and describe the mechanisms behind the workings of financial markets. This reliance has continued to grow with the complexity of the problems considered, and has led to many fruitful examples of cross-pollination of the ideas between the fields. The rapid growth of the financial industry has brought together many researchers with diverse scientific backgrounds who now work in banks, investment management, insurance and other companies which rely on innovation for the growth of their business. In academia as well, we have seen a growing number of cross-disciplinary efforts, from joint seminars and symposia to cross-departmental programs such as those offering the increasingly popular financial engineering degrees.
- Pricing of Securities
Valuation and hedging of financial securities, their derivatives, and structured products.
- Risk Management
Measurement and management of financial risks in trading, banking, insurance, corporate and other applications.
- Portfolio Management
Security selection and optimization, capital allocation, investment strategies and performance measurement.
- Trading and Microstructure
Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making.
- Mathematical Finance
Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods.
- Computational Finance
Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling.
- Statistical Finance
Statistical, econometric and econophysics analyses with applications to financial markets and economic data.
- General Finance
Development of general quantitative methodologies with applications in finance.
Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside of finance.
You can steer your course choices towards those which will be beneficial in a quantitative career. Those courses include (but aren’t limited to):
- Probability – The most fundamental aspect of quant finance is probability. You will not be able to work effectively (or at all!) if you do not understand probabilistic concepts.
- Stochastic Calculus – Stochastic calculus is the toolset through which a quant manipulates the Black-Scholes model for derivatives pricing and its various alternatives. If you wish to price options – you will need a stochastic calculus/analysis backgorund.
- Statistics – If you want to get straight into the quantitative trading aspect (such as working at a fund), you will need a sophisticated level of statistical intuition. Start taking as many stats courses as possible, especially at the upper (300/400) levels.
- Programming – You will spend at least 50% of your time implementing models on the computer as a quant. In a bank this will likely be using C++/Java/C#. In a fund, this will be anything from C++, R, MATLAB or Python depending upon the task.