Mathematical modelling of markets.
11 topics · 12 curated works
No prior grounding assumed.
Equity Market Structure Literature Review, Part II: High Frequency Trading Synopsis
U.S. Securities and Exchange Commission, Division of Trading and Markets · 2014
Synthesises the empirical literature on high-frequency trading, concluding most studies find HFT narrows spreads and adds liquidity in normal markets…
Assumes you know the vocabulary.
Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance
David H. Bailey, Jonathan M. Borwein, Marcos Lopez de Prado & Qiji Jim Zhu · 2014
Given enough trials an impressive backtest can be manufactured from pure noise, so a Sharpe ratio quoted without the number of configurations tried…
+1 more at this level
Primary sources and full treatments.
On a Formula Concerning Stochastic Differentials
Kiyosi Ito · 1951
Derives the chain rule for functions of a stochastic process now known as Ito's Lemma, the calculus that lets a smooth function of a random path be…
+8 more at this level
12 works
U.S. Securities and Exchange Commission, Division of Trading and Markets
Synthesises the empirical literature on high-frequency trading, concluding most studies find HFT narrows spreads and adds liquidity in normal markets while remaining a source of fragility under stress.
David H. Bailey, Jonathan M. Borwein, Marcos Lopez de Prado & Qiji Jim Zhu
Given enough trials an impressive backtest can be manufactured from pure noise, so a Sharpe ratio quoted without the number of configurations tried is not evidence of anything.
link checked 17 Sept 2026Matteo Aquilina, Eric Budish & Peter O'Neill
Uses regulatory data from a UK exchange to measure the resources firms spend racing each other to react to public information a fraction of a millisecond faster, and finds this arms race is a large, continuing tax on liquidity provision with no offsetting gain in market quality.
link checked 17 Sept 2026Kiyosi Ito
Derives the chain rule for functions of a stochastic process now known as Ito's Lemma, the calculus that lets a smooth function of a random path be differentiated even though the path itself is nowhere differentiable.
link checked 17 Sept 2026Robert C. Merton
Derives optimal lifetime consumption and portfolio rules for an investor facing continuously changing asset prices, using stochastic calculus to show that under constant relative risk aversion the optimal portfolio mix does not depend on wealth or horizon.
link checked 17 Sept 2026John C. Cox & Stephen A. Ross
Shows an option can be priced as if all investors were risk-neutral, discounting expected payoffs at the riskless rate under an adjusted probability measure, because a perfectly hedged option position removes the need to know the underlying's true expected return.
Phelim P. Boyle
Introduces simulating many random paths of an underlying asset and averaging the discounted payoff as a way to price options for which no closed-form formula exists, the origin of Monte Carlo methods in finance.
Albert S. Kyle
Models how an informed trader optimally hides behind noise traders, showing market depth and the informativeness of prices are jointly determined by how aggressively the informed trader exploits private information.
Tim Bollerslev
Extends ARCH by letting variance also depend on its own past values, producing a far more parsimonious model of volatility clustering that became the standard workhorse for return series.
link checked 17 Sept 2026Richard K. Lyons
Tests competing microstructure theories against real foreign exchange dealer data and finds order flow -- the signed volume of trades -- explains a large share of exchange rate movements that macroeconomic fundamentals alone cannot.
link checked 17 Sept 2026Shihao Gu, Bryan Kelly & Dacheng Xiu
Benchmarks machine learning methods against traditional linear factor models for predicting stock returns and finds tree-based and neural network models substantially outperform, with nonlinear interactions among a small set of characteristics doing most of the work.
link checked 17 Sept 2026Winston Wei Dou, Itay Goldstein & Yan Ji
Models trading algorithms that learn from repeated market interaction and finds they can converge on collusive, less competitive pricing without any explicit communication or coordination, raising a new kind of antitrust question specific to automated trading.
link checked 17 Sept 2026This subject genuinely sits in more than one domain. These fields approach the same ground with different methods.