Certificate in Quantitative Finance

The Certificate in Quantitative Finance (CQF) is a Financial Engineering program and a finance designation offered by the CQF Institute. CQF provides in-depth, practical training in Mathematical Finance, Financial Modeling, Derivatives and Risk Management. It is half year in duration and is offered class based through Fitch Learning — a London-based provider of training for the financial services industry, owned by the Fitch Group; it is also offered via E-learning.

CQF is designed for in-depth training for individuals working in, or intending to move into Derivatives, Quantitative Trading, Model Validation, Risk Management, Insurance or IT. The CQF is unique in its approach and commitment to the field of real-world quantitative finance.

At all times the program’s focus is on practical implementation of techniques and on the questioning and analysis of models and methods.The CQF was founded in 2003 by Course Directors Paul Wilmott and Paul Shaw. The CQF comprises two levels,[1] each level consisting of three modules; the detail per the side-bar. CQF offers alumni lifelong Learning [2] containing a library of over 600 hours of lectures on every conceivable finance subject. Delivered by some of the most eminent practitioners and academics [according to whom?], the content is ever expanding as additional lectures continually take place. CQF alumni have permanent, unrestricted access to their CQF lectures and the entire Lifelong Learning library.

CQF Module Structure

CQF consists of two levels, each taking approximately three months to complete:

Level I
Building Blocks of Finance
  • The random nature of prices: Examination of data, unpredictability, the need for probabilistic models, drift and volatility.
  • Probability preliminaries: Review of discrete and continuous random variables, transition density functions, moments and important distributions, the Central Limit Theorem.
  • Fokker-Planck and Kolmogorov equations: similarity solutions.
  • Products and strategies: examination of different asset classes, derivatives products and common trading strategies.
  • Applied Itô calculus: Discrete-time random walks, continuous Wiener processes via rescaling and passing to the limit, quadratic variation, Itô integrals and Itô’s lemma.
  • Simulating and manipulating stochastic differential equations.
  • Martingale fundamentals: Conditional expectations, change of measure, stochastic processes as a martingale and tools of the trade.
  • The binomial model: Up and down moves, delta hedging and self-financing replication, no arbitrage, a pricing model and risk-neutral probabilities.
  • Visual Basic for Applications: VBA techniques and tricks for quant finance.
Risk and Return
  • Modern Portfolio Theory: Expected returns, variances and covariances, benefits of diversification, the opportunity set and the efficient frontier, the Sharpe ratio, utility functions and the Black-Litterman Model.
  • Capital Asset Pricing Model: Single-index model, beta, diversification, optimal portfolios, the multi-index model.
  • Portfolio Optimization: Formulation, implementation and use of calculus to solve constrained optimization.
  • Value at risk: Profit and loss for simple portfolios, tails of distributions, Monte Carlo simulations and historical simulations, stress testing and worst-case scenarios.
  • Volatility clustering: Concept and evidence.
  • Properties of daily asset returns: Average values, standard deviations, departures from the normal distribution, squared returns.
  • Properties of high-frequency returns: Five-minute returns contrasted with daily returns, intraday volatility patterns, impact of macroeconomic news, realized variance.
  • Volatility models: The ARCH framework, why ARCH models are popular, the GARCH model, ARCH models, asymmetric
  • ARCH models and econometric methods
Equities & Currencies Derivatives
  • The Black-Scholes model: A stochastic differential equation for an asset price, the delta-hedged portfolio and self-financing
  • replication, no arbitrage, the pricing partial differential equation and simple solutions.
  • Martingales: The probabilistic mathematics underlying derivatives theory, Girsanov, change of measure and Feynman-Kac.
  • Risk-neutrality: Fair value of an option as an expectation with respect to a risk-neutral density function.
  • Early exercise: American options, elimination of arbitrage, modifying the binomial method, gradient conditions, formulation as a free-boundary problem.
  • The Greeks: delta, gamma, theta, vega and rho and their uses in hedging.
  • Numerical analysis: Monte Carlo simulation and the explicit finite-difference method.
  • Further numerical analysis: Crank-Nicolson, and Douglas multi-time level methods, convergence, accuracy and stability.
  • Exotic options: OTC contracts and their mathematical analysis.
  • Derivatives market practice: Examination of common practices and historical perspective of option pricing.
  • Trading Simulator: Trading equity options, options strategies, Greeks, trading volatility
Level II
Fixed Income & Commodities
  • Fixed-income products: Fixed and floating rates, bonds, swaps, caps and floors, FRAs and other delta products.
  • Yield, duration and convexity: Definitions, use and limitations, bootstrapping to build up the yield curve from bonds and swaps.
  • Curve stripping: reference rates & basis spreads, OIS discounting and dual-curve stripping, cross-currency basis curve, cost of funds and the credit crisis.
  • Interpolation methods: piece wise constant forwards, piece wise linear, cubic splines, smart quadratics, quartics, monotone convex splines.
  • Current Market Practices: Money vs. scrip, holiday calendars, business day rules, and schedule generation, day count fractions.
  • Stochastic interest rate models, one and two factors: Transferring ideas from the equity world, differences from the equity world, popular models, data analysis.
  • Calibration: Fitting the yield curve in simple models, use and abuse.
  • Data analysis: Examining interest rate and yield curve data to find the best model.
  • Probabilistic methods for interest rates.
  • Heath, Jarrow and Morton model: Modeling the yield curve. Determining risk factors of yield curve evolution and optimal volatility structure by PCA. Pricing interest rate derivatives by Monte Carlo.
  • The Libor Market Model: (Also Brace, Gatarek and Musiela). Calibrating the reference volatility structure by fitting to caplet or swaption data.
  • SABR Model: Managing volatility risks, smiles, local volatility models, using the SABR model and hedging stability.
  • Arbitrage Free SABR model: Reduction to the effective forward equation, arbitrage free boundary conditions, comparison with historical data and hedging under SABR model.
Credit Products and Risk
  • Credit risk and credit derivatives: Products and uses, credit derivatives, qualitative description of instruments, applications.
  • Structural and Intensity models used for credit risk.
  • CDS pricing, market approach: Implied default probability, recovery rate, default time modeling, building a spreadsheet on CDS pricing.
  • Synthetic CDO pricing: The default probability distribution, default correlation, tranche sensitivity, pricing spread.
  • Implementation: CDO/copula modeling using spreadsheets.
  • Correlation and state dependence: correlation, linear correlation, analyzing correlation, sensitivity and state dependence.
  • Credit Valuation Adjustment (CVA): CVA a guided tour, exposure, modeling exposure, collateral, wrong way risk & right way risk, case study: CDO-Squared.
  • Risk of default: The hazard rate, implied hazard rate, stochastic hazard rate and credit rating, capital structure arbitrage.
  • Copulas: Pricing basket credit instruments by simulation.
  • Statistical methods in estimating default probability: ratings migration and transition matrices and Markov processes
Advanced Topics
  • Stochastic volatility and jump diffusion: Modeling and empirical evidence, pricing and hedging, mean-variance analysis, the Merton model, jump distributions, expectations and worst case analysis.
  • Non-probabilistic models: Uncertainty in parameter values versus randomness in variables, nonlinear equations.
  • Static hedging: Hedging exotic target contracts with exchange-traded vanilla contracts, optimal static hedging.
  • Advanced Monte Carlo techniques: Low-discrepancy series for numerical quadrature. Use for option pricing, speculation and scenario analysis.
  • Energy derivatives: Speculation using energy derivatives and risk management in energy derivatives
  • Cointegration: Modeling long term relationships, statistical arbitrage using mean reversion.
  • Dynamic Asset Allocation: Convexity management, stochastic control, multi-period projection, utility maximization and impact of transaction costs.
  • Forecasting by using option prices: volatility forecasting using historical asset prices and current option prices) inserting option prices into ARCH models, Typical ARCH results.
  • Density forecasting: Criteria for good forecast, estimating risk-neutral densities from option prices, risk-neutral to real-world densities.


See also

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