CQF study plan

Build a Python environment with numpy, pandas, scipy, statsmodels and scikit-learn, and verify each import runs

Derive the Black-Scholes PDE from a delta-hedged portfolio and implement a closed-form call and put pricer, checking put-call parity to within 1e-8

Implement a binomial tree pricer with configurable steps and confirm convergence toward the closed-form price as steps increase

Write down the Girsanov change-of-measure argument for moving from real-world to risk-neutral drift and reproduce the key steps from memory

Simulate geometric Brownian motion paths under both measures and estimate the discretization bias versus the exact lognormal solution

Implement Monte Carlo pricing with antithetic and control variates and quantify variance reduction against plain Monte Carlo

Code a finite-difference Crank-Nicolson solver for the Black-Scholes PDE and compare against the closed-form price on a grid of strikes and maturities

Explain Ito's lemma and apply it to derive the dynamics of log S and of a power of S

Implement the Vasicek and Cox-Ingersoll-Ross short-rate models and simulate paths, checking that CIR stays non-negative

Calibrate a Hull-White one-factor model to a synthetic yield curve and price a caplet

Derive the Heath-Jarrow-Morton no-arbitrage drift condition and state it in your own words

Build a bootstrapping routine that extracts zero rates from a set of par swap rates

Implement a least-squares Monte Carlo American option pricer and validate it against a binomial benchmark

Code the Barone-Adesi-Whaley approximation and compare it with the Longstaff-Schwartz result

Derive and implement delta and gamma by automatic differentiation or bump-and-reval, and check against analytic Greeks

Assess the impact of the polynomial basis choice on Longstaff-Schwartz price stability

Implement a local volatility model from a synthetic implied-volatility surface using the Dupire formula

Calibrate a Heston stochastic-volatility model to a synthetic option chain with a least-squares objective and report parameter recovery

Explain the volatility smile and skew and connect them to the assumptions violated by Black-Scholes

Implement a variance-swap fair-strike calculation under a simple stochastic-volatility model

Implement value-at-risk and expected shortfall by historical simulation and by a parametric normal approach, and compare tail estimates

Code a filtered historical simulation VaR with a GARCH(1,1) volatility filter

Backtest VaR using Kupiec and Christoffersen tests on simulated returns and interpret the p-values

Derive the subadditivity failure of VaR with a two-position counterexample

Build a supervised learning pipeline with proper train, validation and test splits and cross-validation for a return-prediction task

Compare ridge, lasso, random forest and gradient boosting on the same feature set and report out-of-sample metrics

Diagnose overfitting by comparing in-sample and out-of-sample error and by learning curves

Implement a walk-forward backtest that avoids look-ahead bias in feature construction

Implement a simple reinforcement-learning agent for a discrete hedging or allocation task and report cumulative reward against a benchmark policy

Review notes on every prior week and list unresolved weak points with a fix for each

Re-derive the Black-Scholes PDE, the HJM drift condition and the VaR subadditivity counterexample from memory without notes

Complete two timed mock exams under exam conditions and score them