คลังความรู้

The article defines a 60/40 benchmark as a portfolio holding 60% equities and 40% bonds, with periodic rebalancing to restore the target weights. It explains the rationale: stock and bond returns may diversify one another, potentially reducing volatility and…

This curated directory surveys free or freely accessible resources for quantitative finance, grouped into market data, financial engineering, algorithmic trading, programming, and software. It highlights data-quality considerations: foreign-exchange tick…

This introduction explains path signatures as collections of iterated integrals, organized by tensor order. The first level records path increments; second-level terms encode additional ordering information and obey identities linking them to products of…

The article explains why GPU acceleration can shorten deep learning training and compares renting cloud compute with buying a local workstation for quantitative research. It frames the decision around model and parameter-search demands, electricity costs,…

This article applies rough path signatures to a supervised classification task: infer whether a company is based in the United States, United Kingdom, or Germany from its daily closing prices and trading volumes over a year. Stocks are represented as…

This introduction describes tactical asset allocation as a long-horizon portfolio approach that adjusts broad asset-class exposures at relatively infrequent intervals. It contrasts the approach with fixed buy-and-hold allocations and short-term trading, and…

This tutorial explains how to approximate European call and put prices by simulating terminal asset prices under a risk-neutral geometric Brownian motion model. Each simulated price is generated from a standard normal draw; the option payoff is calculated at…

This guide lays out a learning path for aspiring quantitative analysts and financial engineers, whose work often centers on pricing derivatives. It starts with market and product fundamentals, then builds toward risk-neutral valuation, option pricing,…

The document demonstrates a systematic monthly rebalancing strategy using SPY for US equities and AGG for investment-grade bonds. It invests 60% and 40% of initial capital, respectively, at the first month end after the backtest begins. At each later month…

The article classifies common systematic fund approaches by trading style and instrument. It describes trend following as holding positions while trends persist, often accepting frequent small losses in exchange for occasional large moves, and countertrend…

The article considers whether someone without a formal degree can enter high-frequency trading, defining its focus as trading at millisecond or microsecond speeds. It describes the technical work involved: low-latency programming, operating-system and…

This introduction explains how the C++ Standard Template Library organizes data structures and relates them to generic algorithms through iterators. It focuses on containers likely to appear in quantitative finance programs, grouping them into sequence…

The article surveys career paths where people with quantitative, statistical, and software skills can apply machine learning outside traditional asset management. It discusses financial technology use cases such as liquidity prediction, credit assessment,…

This article explains how to implement closed-form Black–Scholes prices for European vanilla calls and puts in Python. It defines the inputs—spot price, strike, risk-free rate, volatility, and time to maturity—and describes the standard normal cumulative…

This career guidance article outlines academic subjects that support work as a quantitative analyst, researcher, trader, or developer. It assumes a numerate degree background and identifies probability as a core foundation, with measure theory as useful…

This article introduces strict stationarity and the Akaike information criterion (AIC) before explaining autoregressive models of order p. An AR model predicts a series from its own prior values and a white-noise term, extending the random-walk idea. For an…

The document introduces the MA(q) time-series model, in which each observation depends on a finite number of current and past white-noise shocks. It explains that the autocorrelation function should cut off beyond lag q, then illustrates model identification…

The document introduces replication as a third way to price a call option in a one-step binomial model, alongside hedging and risk-neutral pricing. The central method is to find a portfolio of other traded instruments whose future payoff matches the option…

The document builds standard Brownian motion from a scaled sequence of random coin tosses. Scaling each step by the square root of its time interval keeps the walk’s quadratic variation finite as the number of steps grows. In the continuous-time limit, the…

The article introduces K-means as a hard clustering method and applies it to daily open, high, low, and close data. It explains that the algorithm assigns each observation to the nearest cluster centroid and iterates assignments and centroid updates to…

This tutorial explains how to map matrix multiplication onto CUDA threads. Each thread computes one output cell by taking the dot product of a row from the first matrix and a column from the second. The article shows how two-dimensional grid and block…

The article demonstrates fitting Gaussian hidden Markov models (HMMs) to simulated returns and S&P 500 daily returns. In the simulation, bullish and bearish periods are generated with different means and variances; a two-state model is then fitted with…

The document describes an intraday pairs strategy that trades SPY against IWM. It estimates a changing hedge ratio with rolling linear regression, constructs a price spread, and standardizes that spread as a z-score. The strategy enters a long spread when…

The document explains how to solve for an option’s implied volatility using Newton-Raphson iteration. The target is the volatility at which a Black-Scholes call price matches an observed market price. Each iteration updates the volatility estimate using the…