THE BEGINNING
Quantitative finance is a relatively new subject which saw its birth at the hands of physicists and other quantitatively trained PHD’s in the early 70’s. Models, concepts, and mathematics have been translated from various disciplines, the major one being physics. Over a short period of time, it has expanded to include a multitude of disciplines each of which have tethered themselves to quantitative finance (a result of technological advancement and innovation) and as a consequence pushed it in their respective directions causing it to expand at an increasing rate.
TIMELINE OF THE BIRTH OF QUANTITATIVE FINANCE:
Today, there are four disciplines that are woven together to make Quantitative Finance:
- Mathematics
- Statistics
- Computer science
- Finance
Each of these disciplines are a required ingredient to create quantitative finance. However, mixing different proportions of them together yields closely related “cousins” of quantitative finance with specific specializations.
Now let us define what quantitative finance is.
DEFINITION
It is a field of applied mathematics concerned with dealing with the financial markets. It is the design and implementation of mathematical models that are used for pricing assets including derivative products, assessing risk, trading, and predicting market moves
Other terms for it, implying that they have very similar proportions of the main ingredients:
- Mathematical finance
- Financial Mathematics
What happens when we alter the proportions of the disciplines? Well, obviously whichever is the dominant discipline becomes the main focus of the subject. Referring back to the “cousins” of quantitative finance here they are:
- Financial Engineering
- Computational Finance
MATHEMATICAL FINANCE, FINANCIAL ENGINEERING, & COMPUTATIONAL FINANCE
Financial Engineering and Computational Finance are the applications of quantitative finance. To be more specific, Mathematical Finance focuses more on using mathematics to analytically develop applications in finance. This inevitably means the level of mathematics used in mathematical finance is rigorous.
It is important to note that Computational Finance aims to find a numerical solution for the analytical models developed in mathematical finance; you’ll see its applications in High frequency trading, algorithmic trading, and quantitative investing.
Meanwhile, Financial Engineering uses the applications developed by mathematical finance and solved numerically by computational finance to solve problems in finance. Evidently enough, the level of mathematics required is not as rigorous as for mathematical finance- the level required is similar to what electric engineering has.
In the past, the first three disciplines (Math, statistics, & Compsci) were essential whilst the last one (finance) wasn’t. However now you need to understand finance, economics, how much the treasury is charging you, fund transfer pricing principals, and the operational model of the bank you’re working at.
A BREAKDOWN OF THE TOPICS IN QUANTITATIVE FINANCE
It is important to understand a basic overview of the topics in quantitative finance, and they are:
Mathematics:
A) Calculus and Linear Algebra
B) Optimization
- Taylor Series
- Markov Processes
C) ODE and PDE
D) Probability
E) Stochastic Calculus & SDE’s
- Martingales
- Brownian Motion
- Stochastic Integrals
- Stochastic Differential Equations
- Ito’s Lemma
- Feynman-Kac
F) Numerical Analysis
G) Binomial Asset Pricing
Statistics:
A) Regression
- OLS (Ordinary Least Squares
- GLM (Generalized Linear Model)
- Logistic
B) Time-series
- ARIMA (Autoregressive integrated moving average)
- GARCH (Autoregressive conditional heteroskedasticy)
- ECM (Error correction model)
C) Nonparametric Regression
- Splines
- Kernel
- Locally Weighted Regression
D) Data Exploration
- Density Estimation
- Normality Tests
- Monte Carlo simulations
- Copulas
E) Data Cleaning and Reduction
- Cluster Analysis
- Stats Theory
Computer Science:
A) Stats Language
- R
- Python
- SAS
- Matlab
- SPSS
B) Programming Language
- Python (Pandas, Numpy, Scipy..)
- C++
C) Memory Management, Functions, Variables, Classes, Loops, If/Else Logic, Operators, Arrays, Reference and Pointers, best practices for writing code
D) Implementation of math and stats knowledge in a program
E) Machine learning
- Random Forest
- Neural Networks
- Decision Tree
- Clustering
- Dimensionality Reduction
- Ensemble
Finance:
A) Equity
- Stock Analysis
- Diversification
- Technical Analysis
- Finance Theory
B) Fixed Income
- Rates Curves
- Pricing
- Duration
- TVM
C) Derivatives
- Black-Scholes
- BDT
- Stochastic Volatility Model
- Volatility Smiles and Theory
D) Portfolio Management & Optimization
- CVaR
- Efficient Frontier
E) Arbitrage Theory and Statistical Arbitrage
F) Risk Management
- VaR
- Statistics
- Credit Risk
- Market Risk
- Liquidity
G) Actuarial Modeling
H) Regulations (eg. BASEL)
Of course this breakdown is far from exhaustive but it shows you what is to be taken from each discipline.
CAREER
The work of a quant can be divided into three primary parts:
- Sell side
- Buy side
- Software and data providing
Sell side: is when an investment bank creates financial products either to:
- match buy orders with their sell orders
- create new innovative financial instruments
Buy side: is when a quant is interested in investing by buying stocks, bonds, and derivatives from the sell side.
At the beginning Quantitative Finance was dominated by mathematical modeling (which is still the core of the subject), but now with the advancement of technology it has been less dominating with the introduction of data science and machine learning.
Careers one can undertake in quantitative finance:
And now finally…
WHO IS A QUANT?
A textbook definition would say, a quant is a person who uses quantitative methods. However in the 70’s it was used to describe individuals who applied mathematics in finance.
Regardless, many recruiters have used the word “Quant” quite liberally, so much so that it has washed away from its original coined meaning and now encompasses everything quantitative not explicitly quantitative finance related occupations.
RECOMMENDATIONS
Furthermore, I’d recommend reading a very interesting and fairly detailed paper by Mark Joshi called, “On Becoming a Quant”.
Whilst we’re on the topic of reading, I’d also suggest you read “My Life as a Quant: Reflections on Physics and Finance”, by Emanuel Derman who was a physicist on Wallstreet. He talks about his challenges in his academic career and his transition to working outside academia and eventually moving to wallstreet. It is a great read and many of the content is food for thought. I particularly would like to point out this quote:
“A good quant must be a mixture, too — part trader, part salesperson, part programmer, and part mathematician.” — Emanuel Derman