Claims on the future, priced today
Finance
Finance is the study of one question asked in a hundred forms: what is a claim on an uncertain future cash flow worth right now? Everything else — accounting, portfolios, derivatives, central banks — is machinery for answering it under different constraints.
Foundations
Almost every finance course starts at the second question. Start at the first: money is a social technology for moving purchasing power across time and trust, and once you see that, interest rates stop being arbitrary.
You will be able to
You can explain where money comes from, who creates it, and why that matters to everything downstream.
- Money as a technologyIf money is just paper, why does anyone accept it?
- Where money comes fromDo banks lend out deposits, or create them?
- Interest as the price of timeWhy should anyone be paid simply for waiting?
- Inflation, real vs nominalWhich of my numbers are lying to me?
Accounting is the language every other module speaks. You do not need to prepare statements; you need to read them adversarially.
You will be able to
You can open any company's annual report and know within minutes how it makes money and how it might die.
- The three statements and how they linkWhy do three documents describe one company?
- Cash flow versus profitHow does a profitable company go bankrupt?
- Ratio analysis and its limitsWhich ratios reveal something, and which just restate the obvious?
- Reading a report adversariallyWhat is management choosing not to show me?
Core
The single most-used calculation in finance. Everything from a mortgage to a sovereign bond is this one idea with different decorations.
You will be able to
You can price any stream of promised cash flows and explain why bond prices fall when rates rise.
- Present value and discountingWhy is a dollar tomorrow worth less than a dollar today?
- Annuities, perpetuities and amortisationWhat am I actually paying in the first year of a mortgage?
- Bond pricing, yield and durationWhy does a 30-year bond fall further than a 2-year when rates move?
- The yield curve and what it predictsWhat is the market saying when the curve inverts?
Where the Mathematics track pays its dividend. Most financial blow-ups are a normal-distribution assumption meeting a non-normal world.
You will be able to
You can describe return distributions honestly — including the tails that standard models pretend do not exist.
- Returns, compounding and log returnsWhy do quants work in logs?
- Volatility, correlation and fat tailsHow often is a '6-sigma event' actually supposed to happen?
- Time series and the efficient market hypothesisIs price movement predictable at all?
Markowitz turned investing from stock-picking into an optimisation problem, and won a Nobel for a result that fits on one page.
You will be able to
You can explain why diversification is the only free lunch, and where the theory quietly breaks.
- Risk, return and diversificationWhy does combining two risky assets reduce risk?
- The efficient frontier and optimisationWhat is the best possible portfolio for a given risk?
- CAPM, beta and factor modelsWhat risk does the market actually pay you to take?
The discipline of turning a story about a business into a number — and being honest about how much of the number is the story.
You will be able to
You can build a defensible valuation and identify which single assumption drives the answer.
- Discounted cash flowWhat is a company worth if I ignore the market entirely?
- Cost of capitalWhat discount rate is defensible, and why is it usually wrong?
- Multiples and relative valuationWhen is a P/E ratio informative rather than decorative?
Advanced
Contracts whose value derives from something else. The pricing argument — replication and no-arbitrage — is one of the most elegant in all of finance.
You will be able to
You can explain why an option has value before expiry, and what Black–Scholes assumes that reality does not supply.
- Forwards, futures and no-arbitrageWhy does the price follow from the absence of free money?
- Options: payoffs and put–call parityWhy is an out-of-the-money option worth anything at all?
- Black–Scholes and replicationHow can you price an uncertain payoff with certainty?
- The Greeks and volatility surfacesWhat does the market's own pricing tell you it expects?
The firm's own decisions: what to invest in, how to fund it, and what to return to owners.
You will be able to
You can reason about how a company should be financed and why the answer is not obvious.
- Capital budgeting: NPV and IRRWhy does IRR mislead exactly when it matters most?
- Capital structure and Modigliani–MillerDoes it matter whether you use debt or equity?
- Dividends, buybacks and signallingWhat does a company communicate by how it returns cash?
Prices are not handed down; they are produced by a mechanism. The mechanism has consequences.
You will be able to
You understand what actually happens to an order after you press buy.
- Order books, liquidity and spreadsWho is on the other side of your trade?
- Market making and high-frequency tradingWhat is the cost of instant liquidity, and who pays it?
- Flash crashes and liquidity spiralsHow does a market with no bad news lose 9% in minutes?
The efficient-market model assumes a rational agent. This module studies the actual one.
You will be able to
You can name the specific ways your own reasoning will cost you money.
- Prospect theory and systematic biasWhy do losses hurt more than equivalent gains please?
- Bubbles, manias and reflexivityCan a price be wrong if everyone agrees on it?
- Designing around your own failure modesWhat process survives contact with your own panic?
Frontier
Where the Mathematics track and this one fully merge. Itô calculus, simulation and the machinery behind modern trading.
You will be able to
You can read the stochastic-calculus literature and implement a pricing model.
- Brownian motion and Itô's lemmaHow do you do calculus on something nowhere differentiable?
- Monte Carlo methodsWhat do you do when there is no closed form?
- Machine learning in markets, honestly assessedWhy do backtests look so much better than live performance?
The environment every asset price sits inside. Rates, inflation, currencies and the institutions that set them.
You will be able to
You can read a central bank statement and understand what it is actually doing.
- Output, employment and the policy toolkitWhat can a central bank actually control?
- Monetary policy, QE and the balance sheetWhat happened to the money created after 2008?
- Exchange rates and international financeWhy do currencies move, and can anyone predict it?
Every crisis was preceded by a risk system that reported everything was fine. Study why.
You will be able to
You can identify the risk that is not in the model — which is the one that matters.
- Value at Risk and its failuresWhat does VaR deliberately not tell you?
- Leverage, margin and forced sellingWhy do sound positions get liquidated?
- 2008, in mechanism rather than moralityWhich specific link in the chain actually broke?
A live experiment in rebuilding finance from cryptographic primitives. Assessed here the same way as everything else: what problem does the mechanism solve, and at what cost?
You will be able to
You can evaluate a crypto system on its mechanism rather than its narrative.
- The double-spend problem and proof of workWhat problem did Bitcoin actually solve?
- Smart contracts and composabilityWhat becomes possible when money is programmable?
- DeFi mechanisms and their failure modesWhich risks were removed, and which were merely renamed?