Quant Concepts Visualised
Curated quantitative finance concepts with interactive visuals. Built to align with your book and “Quant with Vahab”.
Use search and filters to navigate models, pricing, and risk topics.
A loss threshold: “on a normal day, losses should not exceed this amount with X% confidence.”
A real-time state estimator that combines a model and noisy measurements in an optimal way.
Price options on a tree of future prices by working backwards under a risk-neutral world.
The textbook formula for European options in an idealised world with continuous hedging and constant volatility.
A continuous-time random growth model where relative price changes are normal and prices stay strictly positive.
The gap between what the market will pay you and what it will charge you — your immediate cost of trading.
Order types express your priority: do you care more about being filled, or about the price you pay?
Revaluing positions at current market prices to see where you stand right now in P&L and risk terms.
Simple returns measure percentage change; log-returns add nicely over time and align with GBM-style models.
Realised volatility comes from past price moves; implied volatility is the market’s quote for future uncertainty.
No-arbitrage is the pricing consistency rule: you cannot get something for nothing at scale.
A CHF tomorrow is worth less than a CHF today. Discounting converts future cash flows to today.
Duration is first-order rate sensitivity; convexity is the second-order correction.
Leverage amplifies gains and losses; margin is the collateral mechanism that enforces survival constraints.
Liquidity is ‘can you pay today’; solvency is ‘are you worth more than you owe’.
Change of measure turns one drift into another by reweighting paths, while preserving Brownian noise.
Heston couples price and variance dynamics; its characteristic function gives semi-closed-form prices.
Intensity models treat default as a random time with a hazard rate, which can be linked across names via factors.
XVA adjusts idealised prices for counterparty, funding, and capital effects along the exposure profile.
Optimal execution balances market impact and risk over time, typically via quadratic cost control problems.
Filters infer hidden states (value, volatility, regimes) from noisy price or order-flow observations.
DRO optimises performance under the worst distribution in an ambiguity set, not just under a point estimate.
Shrinkage stabilises noisy covariance matrices by pulling them toward structured targets.
Latency creates risk windows; kill-switches turn risk metrics into hard stop conditions in event streams.
A convincing backtest needs power against realistic alternatives and control of data-mining false discoveries.
A no-arbitrage relation linking European calls, puts, spot, and discount factors.
A probability tilt that replaces real-world drift with the risk-free rate so discounted prices become martingales.
Price derivatives by simulating many risk-neutral paths and averaging discounted payoffs.
Use a sequence of traded rates to solve for discount factors and build a zero-coupon curve.
Estimate factor loadings (betas) by regressing asset returns on one or more risk factors.
Covariance measures joint variability in units; correlation rescales it to a dimensionless sensitivity between −1 and 1.
VaR is a loss quantile; CVaR is the average loss beyond that quantile.
Separate contract, data, assumptions, and numerical method so the library can grow without breaking.
Use registries to map product types and models to pricers instead of hard-wiring dependencies.
Snapshot IDs and model IDs make valuations reproducible months later.
A valuation run is defined by its configuration; determinism follows from controlling every input.
Greeks measure sensitivity of prices to well-defined risk factors like spot, rates, and volatility.
Scenarios apply coherent shocks to market snapshots and revalue portfolios for risk and regulation.
P&L explain decomposes daily profit and loss into risk-factor moves, new trades, and residuals.
Day-count, compounding, and calendars connect abstract rates to real cash-flow accruals.
Calibration fits model parameters to market data; validation checks whether the model is fit for purpose.
Power forward curves are not flat lines: they reflect seasonal demand patterns and shaped delivery blocks.
Baseload delivers all hours; peakload focuses on high-demand hours. Shape risk is the difference between them.
Spark and dark spreads measure the margin from turning fuel into power, net of efficiency and CO₂ costs.
Power, gas, and CO₂ prices move together through the merit order: correlation structure drives hedging and risk.
A load profile spreads volume across hours; volume risk is the deviation between forecast and realised load.
Temperature drives heating and cooling demand; a simple weather–load model underpins many power forecasts.
Water in a hydro reservoir is an inventory with an option value: using it today precludes future generation.
Gas storage assets embed an option to shift volume across time, constrained by capacity and injection/withdrawal limits.
Swing contracts grant flexible volume each period within local and global bounds, making them path-dependent real options.
The merit order sorts generation units by marginal cost; where demand meets the stack determines the power price.
Basis risk arises when hedging at a hub or zone that does not perfectly match the physical delivery point.
Protected main plus pull requests and code review is the basic safety net for critical analytics code.
Continuous integration runs tests and checks on every change so broken code never reaches main.
A stable library relies on many small unit tests, fewer integration tests, and a focused regression suite for key trades.
Alembic-style migrations evolve the database safely by applying small, versioned changes that keep old and new code working.
Versioned releases and a changelog let you tie any valuation back to a specific library build and behaviour set.
Structured logs with run IDs and trade IDs turn production errors into actionable, traceable events.
Background workers execute heavy or recurring tasks such as nightly risk, calibration, and data ingestion.
Profiling identifies where time is actually spent so optimisation efforts focus on real bottlenecks, not guesses.
A practical toolkit: unit tests, golden regressions, finite differences, sanity checks, and reproducibility checks.
Golden regressions lock a set of inputs and outputs so any drift in pricing behaviour becomes immediately visible.
Finite differences approximate sensitivities numerically and provide an independent check on analytic Greeks.
Simple economic constraints such as monotonicity, sign, and arbitrage bounds catch deep bugs with minimal effort.
Validating Monte Carlo requires testing the path generator, convergence to benchmarks, and confidence-interval coverage.
Tolerances must reflect trade scale, numerical method, and noise sources, balancing stability against necessary change.
A market snapshot is an immutable bundle of curves, vols, and fixings that defines the pricing environment for a run.
A run ID ties together snapshot, models, library version, and configuration so every number has a recipe.
Raw vendor data is the starting point; curated curves and models are versioned outputs of documented transformation pipelines.
New snapshots capture corrections and backfills without rewriting history, keeping as-used and corrected views side by side.
Replay means re-running a past valuation with the same trades, snapshot, models, and code version to recover the original numbers.
Data lineage traces each reported number back through runs, snapshots, transformations, and raw sources for full auditability.
In control-theoretic terms, market snapshots act as observable system state for the trading and risk engine.
European, American, Asian, and barrier options differ mainly in when and how the payoff depends on the price path.
Forwards and futures lock in a future price; cost-of-carry and convenience yield link them to today’s spot.
Choosing a numeraire (bank account, bond, annuity) induces a measure under which that numeraire-valued price is a martingale.
Black-76 prices options on forwards or futures using forward price, discount factor, and implied volatility as primary inputs.
The smile shows how implied volatility varies with strike; the surface extends this across maturities under no-arbitrage constraints.