Why is it called "Mathematical Finance", not "Statistical Finance"?

[zeptabot_]

About the idea of "Quantitative Finance" in general: Everywhere I look on the Internet, people seem to be saying that Statistics is more relevant to Quant Finance than Mathematics. The quantitative tools in quant finance seem to be based more on upper-year Stat topics (Stochastic process, Multivariate analysis, Time Series Analysis, Probability, Machine Learning) as opposed to upper-year maths (group theory, real analysis, topology). Except for ODE and PDE, which is not used as often then when this occupation first became a thing nowadays anyway.

Dimitri Bianco, the famous quant YouTuber, also said that the best degree for a career in quant finance besides a quant master and a STEM PhD is a Statistics degree.

The similar jobs that are often compared with quants are data scientists (vs quant researchers) and actuaries (vs risk quants), which are obviously more stats-oriented than math-oriented.

So why are most programs still called "Mathematical Finance", not "Statistical Finance"? And why do people still have the impression that quant is a "math" career, not a "stats" career?

I'm just a first-year undergraduate, so there's a lot I don't know and a lot I'm yet to learn. Would love to hear insight from anyone else with experience/knowledge on this topic!

 

[MikeLawrence]

I'm just a first-year undergraduate, so there's a lot I don't know and a lot I'm yet to learn. Would love to hear insight from anyone else with experience/knowledge on this topic!

A good place to start learning is to stop watching YouTibe videos and replace it with interview prep. Bianco is not a serious person in this world. Listen to those with experience on this site, and study hard.

I believe mathematical became the designation because of academic papers. These papers traditionally deal in heavier mathematical methods for pricing options and other topics. While stats is used everywhere, it did not enter this debate. Mathematical finance became the term associated with journals and papers, and programs, and so we loosely study ‘mathematical’ finance.

 

[Chuanzhen Wang]

It's an interesting topic. I've been learning a lot of these two aspects simultaneously recently and have some feelings about it. So I edited a bit more.
I completely agree with your point that statistics skills seem more directly applicable to the work. My mentors during the internships also strongly encouraged me to focus on statistics, even suggesting that pursuing a Statistics PhD could be highly beneficial.

However, I think this shift in emphasis is relatively recent (perhaps becoming prominent only in the last 5-10 years?). Back when quantitative finance was first developing, statistical learning models weren't as mature, computing power was limited, and readily available, clean data (especially alternative data) was much harder to come by. Therefore, rigorous mathematical models were absolutely crucial.

At that time, areas like stochastic analysis, numerical methods, and partial differential equations were extremely useful for pricing derivatives, portfolio management, and risk modeling. These mathematical approaches formed the core of quantitative finance research and practice for a long time(It is actually the same now as Mike said. There is a distinction between academic research and the work carried out in companies). Many of the prominent quantitative finance master's programs were established during that period, so they naturally adopted names like "Mathematical Finance" or "Financial Engineering" based on the dominant methodologies at the time.

As statistics and data science have grown in importance, these programs also haven't stood still. They've rapidly integrated courses in financial statistics, machine learning, deep learning, and programming languages like R or Python into their curricula to adapt to the evolving landscape. For many programs, this integration has been sufficient to equip graduates with the necessary statistical and data analysis skills on top of the foundational mathematical knowledge. So they didn't change their names or set up new projects.

That being said, I think you have a very valid point. It wouldn't surprise me at all if, in the coming years, we start seeing more universities launch programs explicitly named "Statistical Finance" or similar.

To give a personal example, my own university's Applied Statistics master's program has had a dedicated "Financial Statistics" track for quite some time.

 

[zeptabot_]

It's an interesting topic. I've been learning a lot of these two aspects simultaneously recently and have some feelings about it. So I edited a bit more.
I completely agree with your point that statistics skills seem more directly applicable to the work. My mentors during the internships also strongly encouraged me to focus on statistics, even suggesting that pursuing a Statistics PhD could be highly beneficial.

However, I think this shift in emphasis is relatively recent (perhaps becoming prominent only in the last 5-10 years?). Back when quantitative finance was first developing, statistical learning models weren't as mature, computing power was limited, and readily available, clean data (especially alternative data) was much harder to come by. Therefore, rigorous mathematical models were absolutely crucial.

At that time, areas like stochastic analysis, numerical methods, and partial differential equations were extremely useful for pricing derivatives, portfolio management, and risk modeling. These mathematical approaches formed the core of quantitative finance research and practice for a long time(It is actually the same now as Mike said. There is a distinction between academic research and the work carried out in companies). Many of the prominent quantitative finance master's programs were established during that period, so they naturally adopted names like "Mathematical Finance" or "Financial Engineering" based on the dominant methodologies at the time.

As statistics and data science have grown in importance, these programs also haven't stood still. They've rapidly integrated courses in financial statistics, machine learning, deep learning, and programming languages like R or Python into their curricula to adapt to the evolving landscape. For many programs, this integration has been sufficient to equip graduates with the necessary statistical and data analysis skills on top of the foundational mathematical knowledge. So they didn't change their names or set up new projects.

That being said, I think you have a very valid point. It wouldn't surprise me at all if, in the coming years, we start seeing more universities launch programs explicitly named "Statistical Finance" or similar.

To give a personal example, my own university's Applied Statistics master's program has had a dedicated "Financial Statistics" track for quite some time.

Thank you so much for your insights!!
The field of Quant Finance is changing very fast as technology itself evolves, and what we're learning as the "mainstream tools" today might be replaced by something new 5-10 years into the future.
As an aspiring quant who's about to begin my second year at university, would you still suggest studying "traditional" mathematical finance topics like Partial Differential Equations and Stochastic Processes or leaning much more into the Statistics and Computer Science side for getting a quant-relevant position in at least five years (after finishing my Master's), considering how much the field would have changed by then?
And would it be worth it in my undergrad to take the purely theoretical math courses of "Group Theory", "Number Theory" and "Complex Analysis" for the sake of mathematical maturity, if that means replacing some more "useful" CS/Stats courses like Systems Programming, Numerical Methods, and Mathematical Statistics?
(Also for some reason, the Stochastic Process course in my univeristy is offerred by the Stats department rather than Math, and you have to be in a Stats program to be given enrollment priority: STA447H1 | Academic Calendar ) which seems confusing to me