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Explore models, research and experiments from Q4Quant. Open a project to work through its analysis in the member dashboard.

01 / PROJECT

European Option Price and Greeks Calculator

what is the model price of a European option, and what moves it?

Explore project 02 / PROJECT

Volatility Smile and Surface Explorer

how does implied volatility vary across strikes and expiries, and can a surface built from quotes be trusted to price options that are not quoted?

Explore project 03 / PROJECT

Bond Price and Duration Explorer

how does a yield change affect a bond, how good are the quick risk numbers, and does a DV01 hedge actually remove the risk?

Explore project 04 / PROJECT

Portfolio Risk and Diversification Dashboard

which holdings contribute to portfolio risk, and does a risk-minimising allocation deliver lower risk out of sample?

Explore project 05 / PROJECT

Drawdown and Tail-Loss Monitor

how bad have losses on a US equity allocation been, and can the one-number daily risk estimate sent to the board be trusted on the days that matter?

Explore project 06 / PROJECT

Minimal Strategy Backtester

does a 50/200-day moving-average rule on the S&P 500 really beat buy-and-hold once the accounting is done properly, and does the answer survive a different start date and an honest out-of-sample test?

Explore project 07 / PROJECT

Monte Carlo Pricing and Convergence Lab

can the desk's Monte Carlo engine be trusted? When it prints a price with a 95% interval, is the interval honest? Is variance reduction safe? For a real exotic, how much of the uncertainty is numerical and how much is the model?

Explore project 08 / PROJECT

Order-Book and Slippage Calculator

before a bitcoin order is sent to Coinbase, what will it cost against the mid, what drives that cost (spread, depth or fee), and would splitting it over the next minute be cheaper?

Explore project 09 / PROJECT

Polymarket Bitcoin Probability Explorer

for a prediction-market contract such as "BTC above $90k at 08:00 UTC on 30 Oct 2026", what exactly is being priced, how does the price compare with a transparent model and with the BTC options market, and would the model's probabilities have been reliable in the past?

Explore project 10 / PROJECT

TR — Treasury curve risk and hedge validation

This project asks a rates risk manager's question: should a long-duration bond book be hedged with a parallel (10-year DV01-matched) hedge or with a constrained key-rate hedge, and how often should the hedge be reset? The book and hedge bonds are hypothetical, valued on the Federal Reserve's fitted GSW Treasury curve (daily, 1961–2026). The study replicates GSW (2007), Litterman–Scheinkman (1991) and Ho (1992). It then replays 94 monthly hedge reviews with daily revaluation, P&L attribution, an append-only decision ledger, stress scenarios and labelled injected failures.

Explore project 11 / PROJECT

VR — Volatility forecasting and risk-limit calibration

Next-day variance forecasts for **BTCUSDT**, with **ETHUSDT** as external validation, built from Binance 1- and 5-minute bars (2022-01 to 2026-08). The forecasts feed a replayed daily risk-limit service for a hypothetical long BTC position: USD 1m 97.5% ES budget, USD 30m cap, costs assumed at 10 bp.

Explore project 12 / PROJECT

MV: Real-time macro forecasting (US industrial production)

Does a richer model improve a one-month forecast of US industrial production growth when it may only use data published on the forecast date? This project answers that with the Philadelphia Fed Real-Time Data Set (vintage values) and ALFRED release dates.

Explore project 13 / PROJECT

AL — Deposit betas, repricing risk and funding stress (KeyBank N.A.; SVB stress case)

A treasury/ALM workflow built only from public data. It replicates Drechsler, Savov & Schnabl (2017) deposit betas on every FDIC-insured bank. It reconstructs KeyBank N.A.'s balance sheet and repricing ladder from Call Reports and replays 18 quarterly report arrivals (2022Q1–2026Q2) with monthly rate updates, planning NII, measuring EVE and outflow cover, and recording decisions in an append-only ledger. SVB at end-2022 is the stress case.

Explore project 14 / PROJECT

PR — Portfolio risk forecasting and rebalancing control (Select Sector SPDR book)

Replicates Engle & Colacito (2006) — comparing covariance forecasts by the realised variance of the portfolios they build — on the Fama–French 10 industries (daily, 1995–2026), with Ledoit–Wolf shrinkage, Jagannathan–Ma constraints, the DeMiguel et al. 1/N benchmark and a cost break-even. The model chosen on 1995–2018 then runs a monthly-rebalanced, long-only book of the 11 Select Sector SPDR ETFs from 2019-01 to 2026-09 with a holdings and cash ledger (distributions, splits, costs), pre-trade controls, approvals and three labelled drills.

Explore project 15 / PROJECT

FD — Financial filing change and deterioration monitor (50 large U.S. companies)

Replicates Cohen, Malloy & Nguyen (2020, *Lazy Prices*) on SEC filings — cosine, Jaccard and diff similarity of each 10-K/10-Q against its year-earlier counterpart, by document, MD&A and risk-factor section — and tests both channels: next-month returns of changers vs non-changers, and whether the next report deteriorates. Baselines: ratio-only (Piotroski-style) and text-only. An analyst workbench replays 2023–2026 in EDGAR acceptance-time order with a five-review quarterly budget, ranked alerts with excerpts, review states (open / investigate / escalate / dismiss / expired), amendments, late filings, non-reliance events and firm exits.

Explore project 16 / PROJECT

IV — Independent model validation and change control (VR limit model)

Validates the VR project's BTC exposure-limit model the way a model risk function would under SR 26-2 principles: a model inventory, immutable content-addressed candidate artefacts, an independent benchmark engine written from the protocol text, a regression and stress suite (Kupiec, Christoffersen, Basel traffic light, ES residuals, FZ0, look-ahead invariance, a Hull–Suo simulation, a Danielsson et al. risk ratio, Green–Figlewski estimation error), an approval workflow recorded in an append-only ledger, a controlled version change with an injected defect, twelve monthly monitoring checkpoints, and a late-data restatement that cannot rewrite approvals.

Explore project 17 / PROJECT

MM — Inventory-aware market-making research (Coinbase BTC-USD)

This project replicates Avellaneda & Stoikov (2008) on 69 full sessions of Coinbase BTC-USD:

Explore project 18 / PROJECT

EX — Execution replay and transaction-cost diagnostics (Coinbase BTC-USD)

This project replicates Cont, Kukanov & Stoikov (2014) and tests Almgren & Chriss (2001) on 69 full sessions of Coinbase BTC-USD.

Explore project

Learn

Phase 0 primers, Phases 1–2 foundations, and Phase 3 specialisms. Apply what you learn in the separate Projects section.

Calculus IAvailable · 10 topics
  • Functions and Models.
  • Limits and Continuity.
  • Differentiation.
  • Applications of Differentiation.
  • The Integral.
  • Techniques of Integration.
  • Applications of Integration.
  • Parametric Curves and Polar Coordinates.
  • Infinite Sequences and Series.
  • Ordinary Differential Equations.
Probability IAvailable · 5 topics
  • Probability Foundations.
  • Discrete Random Variables.
  • Continuous Random Variables.
  • Multivariate and Derived Distributions.
  • Limit Theorems.
Statistics IAvailable · 8 topics
  • Sampling Distributions and the Normal Family.
  • Statistical Models and Data Reduction.
  • Point Estimation: MOM, MLE, and Optimality Theory.
  • Bayesian Estimation and Posterior Inference.
  • Confidence Intervals and Interval Estimation.
  • Neyman-Pearson Theory and Uniformly Most Powerful Tests.
  • Likelihood Ratio Tests, Wilks' Theorem, and Goodness of Fit.
  • Linear Regression and Analysis of Variance.
Introduction to PythonAvailable · 8 topics
  • Python Foundations.
  • Control Flow and Simple Numerical Programs.
  • Functions and Decomposition.
  • Built-In Data Structures.
  • Files, Exceptions, and Modules.
  • Object-Oriented Programming.
  • Testing, Debugging, and Style.
  • Scientific Python Bridge.
Financial Instruments and MarketsAvailable · 7 topics
  • Markets, Participants, and the No-Arbitrage Principle.
  • Fixed Income: Bonds, Yields, and Interest Rate Risk.
  • Credit: Corporate Bonds, Credit Spreads, and the Default Option.
  • Equities, Money Markets, and FX.
  • Forwards, Futures, Swaps, and Contracts for Difference.
  • Commodities and the Cost-of-Carry World.
  • A First Look at Options: Payoffs, Bounds, and the Binomial Model.
Probability IIAvailable · 5 topics
  • Random Walks on the Integers.
  • Discrete-Time Markov Chains.
  • Branching Processes.
  • The Poisson Process and Renewal Theory.
  • Continuous-Time Markov Chains and Queueing Theory.
Stochastic CalculusAvailable · 6 topics
  • Discrete Martingales and the Gambling Blueprint.
  • Brownian Motion: Construction and Properties.
  • Stochastic Integration and Itô's Formula.
  • Diffusions, SDEs, and the Feynman-Kac Formula.
  • Change of Measure, Girsanov, and Risk-Neutral Pricing.
  • Lévy Processes and Jump Calculus.
Options PricingAvailable · 5 topics
  • Foundations of Computational Option Pricing.
  • Binomial Trees, Barrier and American Options.
  • Monte Carlo Methods and Stochastic Volatility.
  • Path-Dependent Exotics Beyond Barriers.
  • Index, Currency, Futures and Multi-Asset Options.
Linear Algebra IAvailable · 8 topics
  • Vectors, Linear Combinations, and the Dot Product.
  • Solving Linear Systems and Matrix Algebra.
  • Vector Spaces, Subspaces, and the Four Fundamental Subspaces.
  • Linear Transformations, Matrix Representation, and Rank-Nullity.
  • Determinants.
  • Eigenvalues, Diagonalisation, and Dynamical Applications.
  • Symmetric Matrices and the Eigenstructure Toolkit.
  • Introduction to the Singular Value Decomposition.
EconometricsAvailable · 7 topics
  • Regression Diagnostics and Generalized Least Squares.
  • Univariate Time Series: ARMA and Box–Jenkins.
  • Nonstationarity, Unit Roots, and Cointegration.
  • Volatility Estimation Theory.
  • Multivariate Time Series: VAR and Structural Analysis.
  • Panel Data Econometrics.
  • Endogeneity and Instrumental Variables.
Portfolio ManagementAvailable · 7 topics
  • Portfolio Optimisation and Quant Portfolio Construction.
  • Risk Analytics, Fund Management and Model Risk.
  • Index Models and Portfolio Computation.
  • CAPM and Equilibrium Models.
  • Market Efficiency, Behavioral Finance, and Equity Valuation.
  • Portfolio Performance Evaluation.
  • Practitioner Equity Portfolio Management.
Quantitative Risk ManagementAvailable · 9 topics
  • Risk in Perspective and the Regulatory Framework.
  • Loss Distributions, VaR, and Coherent Risk Measures.
  • Empirical Properties of Financial Data and GARCH Volatility Models.
  • Extreme Value Theory.
  • Multivariate Models and Copulas.
  • Market Risk.
  • Credit Risk — Single Name.
  • Portfolio Credit Risk and Credit Derivatives.
  • Operational Risk and Insurance Analytics.
Fixed Income and Interest Rate ModelsAvailable · 11 topics
  • Bond Mathematics and Pricing Fundamentals.
  • The Term Structure of Interest Rates.
  • Duration, Convexity, and Rate Sensitivity.
  • No-Arbitrage Pricing and the Risk-Neutral Framework.
  • Short-Rate Models.
  • Multi-Factor Term Structure Models.
  • The Heath-Jarrow-Morton Framework.
  • Swaps, Futures, and Linear Rate Derivatives.
  • Interest Rate Derivatives and the Volatility Surface.
  • The LIBOR Market Model.
  • Mortgage-Backed Securities and Securitization.
Statistical ArbitrageAvailable · 6 topics
  • Foundations of Relative-Value Trading.
  • Pairs Trading: Distance, Cointegration, and Kalman Filter Methods.
  • The Factor-Residual Model and the S-Score.
  • Signal Research and Alpha Construction.
  • Backtesting and Validation.
  • Execution, Costs, and Portfolio Risk Management.
Advanced Derivatives and Exotic OptionsAvailable · 10 topics
  • The Volatility Smile and the Implied Vol Surface.
  • The Heston Model.
  • Local Volatility.
  • SABR and Volatility Asymptotics.
  • Jumps and Levy Processes.
  • Variance Swaps and Volatility Derivatives.
  • Barrier and Path-Dependent Options.
  • Exotic Cliquets and Structured Products.
  • Local-Stochastic Volatility and Rough Volatility.
  • Pricing in Incomplete Markets.
Convertible ArbitrageAvailable · 5 topics
  • Convertible Anatomy and Markets.
  • Convertible Valuation.
  • Delta Hedging and the Classic Trade.
  • Credit Overlays and Nontraditional Hedges.
  • Portfolio Risk, Financing, and Limits.
Empirical Asset Pricing and Factor InvestingComing soon · 4 topics
  • Testing Asset-Pricing Models.
  • Constructing Factor Portfolios.
  • Factor Portfolios in Practice.
  • Factor Evidence, Decay, and Crowding.
Counterparty Credit Risk and CVAComing soon · 4 topics
  • Counterparty Exposure and Default.
  • CVA, DVA, and Wrong-Way Risk.
  • Netting, Collateral, and Residual Exposure.
  • Dynamic Models and CVA Computation.
Quantitative Research, Data, and BacktestingComing soon · 4 topics
  • Hypotheses, Timestamps, and Point-in-Time Data.
  • Labels, Samples, and Validation Design.
  • Economic Backtest Simulation.
  • Evaluation, Promotion, and Monitoring.
Financial Machine LearningComing soon · 4 topics
  • Financial Labels, Weights, and Memory.
  • Finance-Aware Training and Tuning.
  • Feature Importance and Bet Sizing.
  • Robust Allocation, Regimes, and Monitoring.
Market Microstructure and ExecutionComing soon · 4 topics
  • Market Data and Trading State.
  • Liquidity, Spread, and Market Impact.
  • Orders and Execution Schedules.
  • Post-Trade Analysis and Capacity.
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