Learning path
Quantitative Finance learning path: everything to study, topic by topic
Comprehensive quantitative finance assessment covering stochastic calculus, derivatives pricing, fixed income modeling, risk modeling, statistical methods, numerical methods, and expert quant topics.
Short answer
To learn Quantitative Finance, work through 7 modules and 20 topics in the order they build on each other. It starts with Stochastic Calculus, then moves on to Derivatives Pricing and Fixed Income Modeling. Use the map as a checklist, or measure your level and study only what is missing.
What you will study
Topics are grouped by module. Open one to see its objectives and key concepts.
1 · Stochastic Calculus3 topics
Brownian Motion
Standard Brownian motion properties, filtrations, martingale property, and geometric Brownian motion
Objectives
- Define Brownian motion axioms and verify key properties
- Derive the distribution of geometric Brownian motion paths
Key concepts
- Wiener process
- independent increments
- normal distribution of increments
- filtration
- martingale property
- geometric Brownian motion
Ito Calculus
Ito's lemma, stochastic differential equations, Ito isometry, and quadratic variation
Objectives
- Apply Ito's lemma to transform stochastic differential equations
- Solve standard SDEs arising in financial modeling
Key concepts
- Ito's lemma
- stochastic differential equations
- Ito integral
- Ito isometry
- quadratic variation
- product rule for SDEs
Girsanov Theorem & Change of Measure
Girsanov theorem, Radon-Nikodym derivative, risk-neutral measure, and numéraire changes
Objectives
- Apply Girsanov theorem to change from physical to risk-neutral measure
- Explain the role of numéraire choice in derivative pricing
Key concepts
- Girsanov theorem
- Radon-Nikodym derivative
- risk-neutral measure
- numéraire
- equivalent martingale measure
- market price of risk
2 · Derivatives Pricing3 topics
Black-Scholes Framework
Black-Scholes PDE derivation, closed-form solutions, assumptions, and limitations
Objectives
- Derive the Black-Scholes PDE from a hedging argument and via Feynman-Kac
- Identify when Black-Scholes assumptions break down and the pricing impact
Key concepts
- Black-Scholes PDE
- risk-neutral pricing
- Feynman-Kac formula
- put-call parity
- Black-Scholes assumptions
- lognormal distribution
Binomial & Lattice Models
CRR binomial tree, trinomial trees, American option pricing, and convergence to Black-Scholes
Objectives
- Build a binomial tree to price American and European options
- Determine the early exercise boundary for American puts
Key concepts
- Cox-Ross-Rubinstein model
- risk-neutral probability
- backward induction
- early exercise boundary
- trinomial tree
- convergence to Black-Scholes
Greeks & Dynamic Hedging
Option Greeks, delta-gamma hedging, vega risk, theta decay, and portfolio-level risk management
Objectives
- Compute and interpret all major Greeks for vanilla and simple exotic options
- Design a delta-gamma hedging strategy and quantify residual risk
Key concepts
- delta
- gamma
- vega
- theta
- rho
- delta-gamma hedging
- pin risk
- discrete hedging error
3 · Fixed Income Modeling3 topics
Yield Curve Construction
Bootstrapping, interpolation methods, multi-curve framework, and OIS discounting
Objectives
- Bootstrap a discount curve from swap and deposit rates
- Explain the transition to multi-curve pricing post-LIBOR
Key concepts
- bootstrapping
- cubic spline interpolation
- Nelson-Siegel model
- OIS discounting
- multi-curve framework
- forward rate extraction
Interest Rate Models
Short-rate models, HJM framework, LIBOR market model, and calibration to swaption surfaces
Objectives
- Compare short-rate models and their suitability for different products
- Calibrate Hull-White to the initial term structure and swaption volatilities
Key concepts
- Vasicek model
- Cox-Ingersoll-Ross model
- Hull-White model
- HJM framework
- LIBOR market model
- mean reversion
Bond Pricing & Analytics
Duration, convexity, key rate durations, spread analysis, and callable bond valuation
Objectives
- Calculate and interpret duration, convexity, and key rate durations
- Price a callable bond using OAS analysis
Key concepts
- modified duration
- effective duration
- convexity
- key rate duration
- Z-spread
- OAS
- callable bond pricing
4 · Risk Modeling3 topics
Value-at-Risk Models
Parametric VaR, historical simulation, Monte Carlo VaR, expected shortfall, and backtesting
Objectives
- Implement and compare parametric, historical, and Monte Carlo VaR approaches
- Explain why expected shortfall is a coherent risk measure and VaR is not
Key concepts
- parametric VaR
- historical simulation
- Monte Carlo VaR
- expected shortfall
- coherent risk measures
- VaR backtesting
Credit Risk Modeling
Structural models, reduced-form models, CDS pricing, default correlation, and credit portfolio models
Objectives
- Price a CDS using hazard rates and recovery assumptions
- Explain the role of default correlation in CDO tranche pricing
Key concepts
- Merton model
- reduced-form models
- hazard rate
- CDS pricing
- default correlation
- Gaussian copula
- CDO tranching
XVA Framework
CVA, DVA, FVA, MVA, KVA calculations, wrong-way risk, and impact on derivative pricing
Objectives
- Calculate CVA for an interest rate swap using exposure simulation
- Explain how FVA and MVA change the economics of uncollateralized trades
Key concepts
- CVA
- DVA
- FVA
- MVA
- KVA
- wrong-way risk
- exposure profiles
- netting and collateral
5 · Statistical Methods3 topics
Time Series Analysis
ARIMA, cointegration, regime switching, mean reversion tests, and autocorrelation analysis
Objectives
- Fit and validate an ARIMA model for financial return prediction
- Test for cointegration and build a mean-reverting pairs strategy
Key concepts
- ARIMA
- cointegration
- Augmented Dickey-Fuller test
- regime switching
- Hurst exponent
- autocorrelation function
Volatility Modeling
Local volatility, stochastic volatility, Heston model, SABR, volatility surface construction
Objectives
- Construct a local volatility surface from market option prices using Dupire
- Calibrate the Heston model and explain its advantages over local volatility
Key concepts
- implied volatility surface
- local volatility
- Dupire equation
- stochastic volatility
- Heston model
- SABR model
- volatility smile
Model Calibration & Validation
Objective functions, regularization, cross-validation, overfitting, and model risk assessment
Objectives
- Design a calibration procedure with regularization to prevent overfitting
- Assess model risk through parameter sensitivity and out-of-sample testing
Key concepts
- least-squares calibration
- regularization
- cross-validation
- overfitting detection
- model risk
- parameter stability
6 · Numerical Methods3 topics
Monte Carlo Simulation
Path generation, discretization schemes, convergence analysis, and pricing by simulation
Objectives
- Implement Monte Carlo pricing with Euler-Maruyama discretization
- Analyze convergence rates and distinguish strong from weak convergence
Key concepts
- Euler-Maruyama scheme
- Milstein scheme
- path generation
- convergence rate
- strong vs weak convergence
- pricing by simulation
Finite Difference Methods
Explicit, implicit, and Crank-Nicolson schemes for PDE-based option pricing
Objectives
- Implement Crank-Nicolson to solve the Black-Scholes PDE for American options
- Analyze stability and convergence properties of finite difference schemes
Key concepts
- explicit scheme
- implicit scheme
- Crank-Nicolson
- stability conditions
- boundary conditions
- grid design
Variance Reduction Techniques
Antithetic variates, control variates, importance sampling, stratified sampling, and Longstaff-Schwartz
Objectives
- Apply antithetic and control variates to reduce Monte Carlo pricing variance
- Implement Longstaff-Schwartz for American option pricing by simulation
Key concepts
- antithetic variates
- control variates
- importance sampling
- stratified sampling
- Longstaff-Schwartz algorithm
- quasi-Monte Carlo
7 · Expert Quant2 topics
Exotic Derivatives Pricing
Barrier options, Asian options, lookback options, cliquets, and model choice for exotics
Objectives
- Select the appropriate pricing model for different exotic payoffs
- Explain why local volatility and stochastic volatility give different exotic prices
Key concepts
- barrier options
- Asian options
- lookback options
- cliquet options
- autocallables
- model dependency
- smile risk for exotics
Portfolio Optimization & Quant Strategies
Mean-variance optimization, Black-Litterman, risk parity, factor models, and systematic strategies
Objectives
- Implement Black-Litterman with investor views and evaluate vs mean-variance
- Design a risk parity portfolio and compare factor exposure to cap-weighted
Key concepts
- mean-variance optimization
- Black-Litterman model
- risk parity
- factor models
- shrinkage estimators
- transaction cost modeling
Levels: Junior, Mid, Senior, and Expert
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Frequently asked questions
Where should I start studying Quantitative Finance?
Start with Stochastic Calculus: Brownian Motion, Ito Calculus, and Girsanov Theorem & Change of Measure. The map orders topics by what they depend on, so each one prepares the next.
How long does a full Quantitative Finance assessment take?
A full assessment of this path takes about 55 minutes. Study time depends on where you start; a diagnostic shows which topics you can skip.
Do I need an account to use this page?
No. The map, objectives and key concepts are open. You only need an account to be measured, get your gap by topic and receive a plan.