May I seek your opinion on which electives should I take over the course of my 4-year undergraduate degree?
TLDR: Should I pursue the measure-theoretic probability path or the Statistics/Computer Science path?
Some context about myself:
I am currently a freshman attending a university in Singapore and my major is Quantitative Finance (QF). (Some of you may irk at the sight of a bachelor's degree in QF, I get it...)
A detailed list of my major requirements (the modules I MUST/HAVE/AM/WILL take) includes:
- Calculus (the contents are similar to the United States' Calculus 1 content, plus a tiny bit on Real Analysis)
- Linear Algebra 1 (the usual undergraduate linear algebra stuff; eigenvalues, diagonalization, rank, linear transformation between Euclidean spaces)
- Python programming
- A module on finance which covers: financial statement analysis, long-term financial planning, time value of money, risk and return analysis, capital budgeting methods and applications, common stock valuation, bond valuation, short-term management and financing.
- Multivariable Calculus (the equivalent of US' Calculus 3)
- Real Analysis. Major topics: Basic properties of real numbers, supremum and infimum, completeness axiom. Sequences, limits, monotone convergence theorem, Bolzano-Weierstrass theorem, Cauchy's criterion for convergence. Infinite series, Cauchy's criteria, absolute and conditional convergence, tests for convergence. Limits of functions, fundamental limit theorems, one-sided limits, limits at infinity, monotone functions. Continuity of functions, intermediate-value theorem, extreme-value theorem, inverse functions
- Numerical Analysis
- Probability (calculus-based probability)
- Investment Instruments: Theory and Computation which focuses on the basic paradigms of modern financial investment theory, to provide a foundation for analysing risks in financial markets and to study the pricing of financial securities. Topics will include the pricing of forward and futures contracts, swaps, interest rate and currency derivatives, hedging of risk exposures using these instruments, option trading strategies and value-at-risk computation for core financial instruments. A programming project will provide students with hands-on experience with real market instruments and data.
- Mathematical Finance 1 covering: the basics of financial mathematics and targets all students who have an interest in building a foundation in financial mathematics. Topics include basic mathematical theory of interest, term structure of interest rates, fixed income securities, risk aversion, basic utility theory, single-period portfolio optimization, basic option theory, emphasizing on mathematical rigour.
- Regression Analysis
- Ordinary Differential Equation, that includes the mathematical analysis of ODE
- Linear and Network Optimization or Nonlinear programming
- A couple of Business oriented modules
- Financial Modelling: which equips me with the knowledge of modelling financial process for the purpose of pricing financial derivatives, hedging derivatives, and managing financial risks. The emphasis of this module will be on numerical methods and implementation of models which includes: implied trinomial trees, finite difference lattices, Monte Carlo methods, model risk, discrete implementations of short rate models, credit risk and value-at-risk.
- Mathematical Finance 2: which provides me with in-depth knowledge of pricing and hedging of financial derivatives in equity, currency and fixed income markets. Major topics include fundamental of asset pricing, basic stochastic calculus, Ito’s formula, Black-Scholes models for European, American, path-dependent options such as Barrier, Asian and Lookback options, as well as multi-asset options and American exchange options.
Anyway, with this context, what are your opinions on the elective (unrestricted) modules I should take to complement my studies?
Option 1: Follow up with 3 more mathematical analysis modules, which covers differentiability, Riemann integrals, metric spaces, an analysis treatise on multivariable calculus, measure theory?
Option 2: Follow up with more statistics and computer science modules which exposes me to mathematical statistics, applied time series analysis, statistical learning, machine learning, designing/ analysis of algorithms, data analysis etc.
I also plan to pursue postgraduate studies, either a Masters in Financial Engineering or PhD (that's quite some time away but I want to be in a position best suited to further my studies).
Correct me if I am wrong, but from my premature understanding of QF, I understand that stochastic calculus/ stochastic analysis are used for areas such as option pricing and model validation whereas one can apply his/her knowledge of statistics and Computer Science on algorithmic trading/ HFT. Currently, I am interested in algorithmic trading - I'm working on a mean reversion theory project in university. However, since I am unsure of which area of QF I am interested in, I do not want to close my doors unnecessarily....
I think I have already said quite a bit so I'll stop here for now.
Nevertheless, thank you for reading and I would like to hear what you have to say!