MIT 18.S096 — Introduction to Mathematical Finance (Lecture 1, Part I)

ELI5/TLDR

MIT’s mathematical finance course (18.S096) pairs a math track with guest lectures from people who actually work at hedge funds and banks. The instructors — Vasily Strela (a quant at RBC) and Peter (a statistician who worked at hedge funds) — both started in pure academia and drifted toward finance. The class assumes you know linear algebra and stats but nothing about finance, and it covers everything from Black-Scholes to machine learning, with practitioners from BlackRock, Two Sigma, Millennium, and Kalshi dropping in to teach individual sessions.

The Full Story

The People Teaching This

Vasily Strela got his PhD from MIT’s math department in 1992 under Gil Strang. His thesis was about wavelets and signal processing — nothing financial whatsoever. He spent a few years as a math professor, then crossed over to become a quant. He’s been at Morgan Stanley and now runs fixed-income quants at RBC.

Peter has a PhD in mathematical statistics from UC Berkeley. He was deep in the theoretical weeds when he wandered into a class at the Haas School of Business and something clicked. He taught at Harvard’s statistics department, then moved to MIT Sloan. A consulting client wanted to hire him to build a trading program for international equities; they ended up becoming partners instead. He worked with hedge funds for years, including IKOS in Cyprus, before returning to academia about 11-12 years ago to co-teach this course.

Both followed the same arc: pure math, then the realization that finance is where the interesting problems live. The class is built on that premise.

The Structure

The course alternates between math lectures (taught by Peter) and applied finance lectures (taught by industry guests). Prerequisites are linear algebra, statistics, and calculus. No finance background needed.

The guest speaker lineup reads like a Rolodex of institutional finance:

• Jeff Shen from BlackRock on quantitative equity investing
• Stefan Andreev from Two Sigma on principal component analysis in finance
• Andrew Gustavsson from Mizuho on rates, swaps, bonds, and curve construction
• James Sheppard from Quantile Technologies (now part of the London Stock Exchange) on optimizing derivative portfolios
• Tarek Mansoor and Luna Lopez from Kalshi on building their prediction market exchange
• Ross Garon from Millennium on systematic investing
• Andrew Lo from MIT on applying computational finance to biomedicine
• John Hull — described as “legendary in derivatives space” — on machine learning

Vasily himself covers Black-Scholes. Jake (the third instructor, briefly mentioned) handles portfolio optimization.

The Kalshi Side Story

Peter taught Tarek and Luna in statistics classes. They went on to create Kalshi, a futures exchange for discrete events — binary bets on whether something will or will not happen. Peter puts this in context: the Commodity Futures Trading Commission has seen maybe 50 exchanges come and go over the years, the Chicago Mercantile Exchange being the most important. Two former students building a new one from scratch is, as he understates it, “rather impressive.”

The R Situation

The course uses R, not Python, for data analysis. Peter is upfront about this:

“I think most students here probably are Python experts. I am not a Python expert, so I use R.”

R gives access to statistical packages for things like nonlinear volatility models and regime modeling. The course provides RStudio Cloud access (free, browser-based) and pre-built R notebooks that pull financial data from Yahoo Finance and the Federal Reserve Economic Database, which houses about 80,000 time series.

The Market Oddities

Peter walks through several financial time series to make a broader point about how markets can do things that seem impossible until they happen.

Bitcoin: The course’s time series starts around when MIT was founded — well, when the class began. An MIT alum gave incoming students $100 in Bitcoin. Years later, some still had their keys. Others had lost them. Peter admits to being a “complete skeptic” then, and still one now, but acknowledges “there’s obviously a great potential there.”

NVIDIA: They displayed NVIDIA’s chart in last year’s notes. Since then, it rose “rather dramatically.” Peter notes that detecting bubbles and predicting when they burst is “very challenging” — which is academic for “nobody can do it reliably.”

Crude Oil Futures (2020): The price went negative. Not a little negative — significantly negative. Brokers had not programmed the possibility of negative prices into their systems. People holding thousands of contracts suddenly owed money to the exchange. The systems simply did not account for it.

“The financial markets offer these cases where surprising, seemingly impossible events can occur, such as negative interest rates. When I was studying finance, the thought of negative interest rates was just considered an impossibility.”

This is the real thesis of the opening lecture, slipped in casually at the end: the things finance textbooks call impossible have a habit of happening.

Claude’s Take

This is a first-day orientation lecture, so there is not much to fact-check — it is mostly logistics, introductions, and a preview of coming attractions. But a few things stand out.

The guest speaker lineup is genuinely impressive. Jeff Shen is a senior figure at BlackRock. Ross Garon runs a major division at Millennium, one of the most successful multi-strategy hedge funds. John Hull wrote the standard derivatives textbook used globally. Andrew Lo is one of the most cited finance academics alive. This is not a course padding its roster with mid-level practitioners.

Peter’s anecdotes about negative oil prices and negative interest rates are well-chosen. These are real historical events that broke models and cost people real money. The broader lesson — that model assumptions are assumptions, not laws of physics — is probably the single most important thing a mathematical finance student can internalize, and it is encouraging that they lead with it.

The R-over-Python choice is a bit dated but defensible for a statistics-heavy course. R’s ecosystem for time series analysis and financial econometrics is still strong. That said, most quant shops run Python, so students will need to translate eventually.

One thing the lecture does not address, because it is an intro, is the survivorship bias baked into having successful quants teach the course. People who left academia for finance and thrived naturally believe the path is worth taking. The ones who flamed out are not giving guest lectures at MIT. This is not a criticism of the course — it is just the nature of the genre.

Overall, this is a solid, unpretentious opening to what looks like a well-structured course. The instructors are candid about their backgrounds and the course’s limitations. No overselling. No claims that you will be printing money after 12 lectures. Just: here is the math, here are the people who use it, here is what the world actually looks like.