Quantitative Finance Curriculum for an ASA
I have decided that I’d rather not pursue the FSA designation but instead improve my actuarial tech stack to an “actuarial quant” tech stack. I’ve grown fond of quantitative finance but feel the SOA exams for quantitative finance are particularly lacking in mathematics. So I decided to ask ChatGPT to design a self-study curriculum to improve myself not only in actuarial science but also in quantitative finance. I think this will improve my knowledge of asset and liability modeling and improve myself mathematically as well. I think ChatGPT overloaded the curriculum with advanced topics in quantitative finance so I probably won’t have to go too in depth with those topics. I know the actuarial topics are a little light though. If any quant is reading this, do I need to go through the whole gauntlet of quantitative finance topics in here? Any feedback is appreciated!
Below is the curriculum that ChatGPT wrote up (112 weeks of study!):
Module 1 — Mathematical Foundations: Linear Algebra, Real Analysis, Measure-Theoretic Probability, and Fourier/Functional Tools
Week 1: Linear Algebra: Vector Spaces, Bases, Inner Products, and Projections
Topics: Vector spaces, subspaces, bases and dimension; norms and inner products; orthogonal projections; least squares geometry.
Reading (book → chapters/sections): Axler Ch 1–2.
Coding deliverable: Implement projection operators and orthogonal decomposition; validate numerically; add unit tests.
Time: 6–10 hrs
Week 2: Linear Algebra: Linear Maps, Rank-Nullity, and Change of Basis
Topics: Linear maps and matrix representations; rank-nullity theorem; change-of-basis matrices; invariance and coordinate systems.
Reading (book → chapters/sections): Axler Ch 3; Searle matrix basics (optional).
Coding deliverable: Implement change-of-basis utilities and rank/null-space diagnostics; random-matrix experiments.
Time: 6–10 hrs
Week 3: Numerical Linear Algebra: Conditioning, Stability, and LU Factorization with Pivoting
Topics: Condition numbers; stability and backward error; LU factorization; partial pivoting; solving linear systems robustly.
Reading (book → chapters/sections): Trefethen & Bau §1–3; Higham (selected on stability).
Coding deliverable: Implement LU with partial pivoting; compare residuals/condition numbers vs numpy.linalg.solve; write stability notes.
Time: 6–10 hrs
Week 4: Numerical Linear Algebra: QR Decomposition and Least Squares via Orthogonality
Topics: Householder QR; least squares; normal equations pitfalls; numerical stability.
Reading (book → chapters/sections): Axler Ch 4; Trefethen & Bau §4.
Coding deliverable: Implement Householder QR; solve ordinary least squares; compare to normal equations under ill-conditioning.
Time: 6–10 hrs
Week 5: Eigenvalue Methods: Power Iteration, Rayleigh Quotient, and Spectral Intuition
Topics: Eigenvalues/eigenvectors; diagonalization; power iteration; Rayleigh quotient; convergence intuition.
Reading (book → chapters/sections): Axler Ch 5; Trefethen & Bau §5.
Coding deliverable: Implement power iteration and Rayleigh quotient iteration (simple); apply to covariance matrices; convergence diagnostics.
Time: 6–10 hrs
Week 6: Symmetric Matrix Theory: Spectral Theorem, Positive Definiteness, and Cholesky Decomposition
Topics: Spectral theorem; positive semidefinite/positive definite; Cholesky; correlation matrices and numerical issues.
Reading (book → chapters/sections): Axler Ch 6; Higham (selected) for stability.
Coding deliverable: Build Cholesky-based correlated simulation harness; PD checks; repair near-PD matrices (eigenvalue clipping).
Time: 6–10 hrs
Week 7: Singular Value Decomposition and Principal Component Analysis for Factor Extraction
Topics: SVD; low-rank approximation; PCA; factor extraction for yield curve movements.
Reading (book → chapters/sections): Trefethen & Bau §6; Strang (selected).
Coding deliverable: Implement PCA from scratch; apply to yield curve change data (synthetic/public); interpret first 3 factors.
Time: 6–10 hrs
Week 8: Matrix Calculus and Gradient Checking for Quantitative Optimization
Topics: Matrix derivatives; gradients/Jacobians/Hessians; finite-difference checks; portfolio variance gradients; regression objectives.
Reading (book → chapters/sections): Magnus & Neudecker (selected) + Boyd & Vandenberghe (selected).
Coding deliverable: Create gradient-check notebook; implement mean-variance objective gradients and verify against finite differences.
Time: 6–10 hrs
Week 9: Real Analysis: Sequences, Limits, Completeness, and Epsilon Proof Techniques
Topics: Convergence of sequences; completeness; supremum/infimum; epsilon proofs; numerical convergence pitfalls.
Reading (book → chapters/sections): Abbott Ch 1–2.
Coding deliverable: Maintain proof notes; code numerical convergence demos highlighting floating-point pitfalls.
Time: 6–10 hrs
Week 10: Real Analysis: Continuity, Uniform Continuity, and Compactness
Topics: Continuity vs uniform continuity; compactness; Heine–Borel; applications to optimization.
Reading (book → chapters/sections): Abbott Ch 3–4.
Coding deliverable: Build counterexample gallery in code; visual demonstrations of uniform continuity and compactness.
Time: 6–10 hrs
Week 11: Real Analysis: Differentiation, Mean Value Theorem, Taylor Approximations, and Error Bounds
Topics: Differentiation; mean value theorem; Taylor series; remainder bounds; Lipschitz conditions.
Reading (book → chapters/sections): Abbott Ch 5.
Coding deliverable: Implement Taylor error study for exp/log; estimate Lipschitz constants numerically.
Time: 6–10 hrs
Week 12: Integration Foundations: Riemann Integration, Improper Integrals, and Quadrature Motivation
Topics: Riemann integration; improper integrals; numerical quadrature motivation; accuracy vs step size.
Reading (book → chapters/sections): Abbott Ch 6; Strang numerical integration sections.
Coding deliverable: Implement trapezoid/Simpson; compare to scipy.integrate.quad; error vs step size plots.
Time: 6–10 hrs
Week 13: Measure Theory for Probability: Sigma-Algebras, Measures, and Measurable Functions
Topics: Sigma-algebras; measures; measurable functions; Lebesgue integral intuition for probability.
Reading (book → chapters/sections): Folland Ch 1 (selected) or Williams Ch 1–2.
Coding deliverable: Implement finite-set sigma-field generator; partition-based integration demo.
Time: 6–10 hrs
Week 14: Convergence Theorems: Monotone Convergence, Dominated Convergence, and Lp Convergence
Topics: Modes of convergence; MCT/DCT; Lp spaces; implications for Monte Carlo estimators.
Reading (book → chapters/sections): Williams Ch 3–4.
Coding deliverable: Simulate almost sure vs in-probability vs Lp convergence; DCT illustration with random variables.
Time: 6–10 hrs
Week 15: Functional Analysis Essentials: Hilbert Spaces, Projections, Operator Norms, andConditional Expectation as Projection
Topics: Hilbert space structure; orthogonal projections; operator norms; conditional expectation as L2 projection.
Reading (book → chapters/sections): Kreyszig functional analysis (selected) + Williams (projection view).
Coding deliverable: Implement projection-as-conditional-expectation demo; operator norm experiments; short explanatory memo.
Time: 6–10 hrs
Week 16: Fourier Analysis Essentials: Convolution, Spectral Methods, and Time Series Connections
Topics: Fourier transform intuition; convolution; spectral density/periodogram; filtering; PDE/time series connections.
Reading (book → chapters/sections): Strang (FFT/spectral) + optional Stein & Shakarchi (selected).
Coding deliverable: Implement FFT-based convolution; compute periodogram for returns; simple low-pass filter; interpret effects.
Time: 6–10 hrs
Week 17: Probability Foundations: Conditional Expectation, Jensen's Inequality, Tower Property, and Martingale Preview
Topics: Conditional expectation properties; Jensen; tower property; martingale definition and examples preview.
Reading (book → chapters/sections): Williams conditional expectation sections.
Coding deliverable: Estimate conditional expectations by regression; verify tower property numerically; write one-page summary.
Time: 6–10 hrs
Week 18: Limit Theorems: Law of Large Numbers, Central Limit Theorem, and Characteristic Functions
Topics: LLN and CLT; characteristic functions; weak convergence intuition; heavy-tail behavior and consequences.
Reading (book → chapters/sections): Casella & Berger asymptotics sections + Williams (selected).
Coding deliverable: Simulate CLT under heavy tails; empirical characteristic function plots; compare convergence rates.
Time: 6–10 hrs
Module 2 — Statistics and Optimization Foundations: Inference, Generalized Linear Models, Regularization, and Convex Optimization
Week 19: Statistical Inference: Likelihood Theory, Sufficiency, Exponential Families, and Maximum Likelihood Estimation
Topics: Likelihood; sufficient statistics; exponential families; maximum likelihood estimation; profiling; invariance.
Reading (book → chapters/sections): Casella & Berger likelihood and maximum likelihood estimation chapters.
Coding deliverable: Implement MLE for Normal/Poisson/Gamma; profile likelihood plots; interpretation notes.
Time: 6–10 hrs
Week 20: Statistical Inference: Hypothesis Testing, Likelihood Ratio Tests, Wald Tests, Score Tests, and Power Analysis
Topics: Testing frameworks; LR/Wald/Score tests; p-values; type I/II errors; power; multiple testing overview.
Reading (book → chapters/sections): Casella & Berger testing chapters.
Coding deliverable: Simulate power curves; compare LR vs Wald; create a testing report with charts.
Time: 6–10 hrs
Week 21: Asymptotic Statistics: Delta Method, Fisher Information, Large-Sample Confidence Intervals, and Bootstrap Coverage
Topics: Asymptotic normality; Fisher information; delta method; bootstrap confidence intervals; coverage studies.
Reading (book → chapters/sections): Casella & Berger asymptotics + ISLR resampling (supporting).
Coding deliverable: Bootstrap vs asymptotic confidence intervals; coverage simulation; memo of findings.
Time: 6–10 hrs
Week 22: Regression Modeling: Ordinary Least Squares Diagnostics, Multicollinearity, and Ridge Regression
Topics: OLS assumptions; diagnostics; leverage/influence; multicollinearity; ridge regression; bias-variance tradeoff.
Reading (book → chapters/sections): ISLR regression chapter; Searle regression (optional).
Coding deliverable: Build OLS and ridge; variance inflation demonstration; diagnostics; unit tests.
Time: 6–10 hrs
Week 23: Generalized Linear Models: Poisson Regression for Claim Counts and Logistic Regression for Classification
Topics: Generalized linear model framework; link functions; deviance; iteratively reweighted least squares; interpretation; overdispersion overview.
Reading (book → chapters/sections): McCullagh & Nelder (selected) or ISLR classification; Loss Models frequency sections (supporting).
Coding deliverable: Implement iteratively reweighted least squares Poisson GLM from scratch; compare to statsmodels.
Time: 6–10 hrs
Week 24: Regularization and High-Dimensional Modeling: Lasso, Elastic Net, Cross-Validation, and Stability
Topics: L1/L2 regularization; coordinate descent for lasso; elastic net; cross-validation; stability under correlation.
Reading (book → chapters/sections): ISLR regularization; ESL regularization (selected).
Coding deliverable: Implement coordinate descent lasso; compare to sklearn; coefficient stability analysis.
Time: 6–10 hrs
Week 25: Bayesian Modeling Foundations: Conjugate Priors, Posterior Computation, and Simple Markov Chain Monte Carlo
Topics: Conjugate priors; posterior computation; Monte Carlo estimation; Metropolis–Hastings overview; diagnostics.
Reading (book → chapters/sections): Wasserman Bayesian sections + Gelman (selected).
Coding deliverable: Implement conjugate Poisson–Gamma; implement Metropolis–Hastings sampler for 1D posterior; diagnostics plots.
Time: 6–10 hrs
Week 26: Model Selection and Resampling: Cross-Validation, Bootstrap, Time-Series Splits, and Leakage Avoidance
Topics: Cross-validation variants; bootstrap; leakage; time-series CV; nested CV overview.
Reading (book → chapters/sections): ISLR resampling.
Coding deliverable: Build reusable cross-validation framework including time-series split; demonstrate leakage failure and fix.
Time: 6–10 hrs
Week 27: Numerical Computing: Floating-Point Arithmetic, Cancellation, Conditioning, and Stable Reformulations
Topics: Floating point; rounding; cancellation; conditioning; stable reformulations; backward/forward error.
Reading (book → chapters/sections): Higham (selected) + Trefethen & Bau conditioning sections.
Coding deliverable: Numerical stability notebook; rewrite unstable formulas; quantify error improvements.
Time: 6–10 hrs
Week 28: Root Finding Methods: Bracketing, Newton’s Method, Secant Method, and Robust Implied Volatility Solving
Topics: Root finding; convergence; bracketing safeguards; stopping criteria; monotonicity concerns; implied vol solving.
Reading (book → chapters/sections): Nocedal & Wright (selected) + Burden & Faires (selected).
Coding deliverable: Build robust implied volatility solver with bracketing; test across moneyness/maturity grid.
Time: 6–10 hrs
Week 29: Convex Optimization: Convex Sets and Functions, Duality, Karush–Kuhn–Tucker Conditions, and Portfolio Optimization
Topics: Convex sets/functions; duality; KKT; constrained optimization; portfolio applications.
Reading (book → chapters/sections): Boyd & Vandenberghe Ch 2–5.
Coding deliverable: Solve constrained mean-variance optimization; verify KKT; compare to cvxopt/scipy.
Time: 6–10 hrs
Week 30: Proximal Algorithms and Alternating Direction Method of Multipliers: Practical Sparse Optimization
Topics: Proximal gradient; ADMM; lasso; elastic net; convergence and tuning intuition.
Reading (book → chapters/sections): Boyd ADMM notes + Boyd (selected).
Coding deliverable: Implement proximal gradient lasso and a simple ADMM lasso; benchmark vs sklearn.
Time: 6–10 hrs
Week 31: Iterative Methods for Large Systems: Conjugate Gradient, Preconditioning, and Sparse Linear Algebra
Topics: Sparse matrices; conjugate gradient; preconditioning; stopping rules; applications to PDE discretizations.
Reading (book → chapters/sections): Trefethen & Bau iterative sections.
Coding deliverable: Implement conjugate gradient; apply to Poisson discretization; profile runtime and iterations.
Time: 6–10 hrs
Week 32: Monte Carlo Simulation: Variance Reduction Techniques and Quasi-Monte Carlo with Low-Discrepancy Sequences
Topics: Control variates; antithetic variates; stratification; importance sampling overview; Sobol sequences; quasi-Monte Carlo behavior.
Reading (book → chapters/sections): Glasserman Ch 4–6.
Coding deliverable: Implement control variate and Sobol quasi-Monte Carlo for option pricing; compare variance and runtime.
Time: 6–10 hrs
Week 33: Reproducible Scientific Computing: Experiment Design, Packaging, Profiling, and Continuous Integration
Topics: Experiment runners; configuration management; logging; profiling; vectorization; unit tests; continuous integration pipelines.
Reading (book → chapters/sections): Clean Code (selected) + Kleppmann (selected).
Coding deliverable: Create experiment runner template; add logging and benchmarks; set up pytest + GitHub Actions.
Time: 6–10 hrs
Week 34: Ordinary Differential Equations and Partial Differential Equations: Numerical Schemes and Connections to Derivative Pricing
Topics: Systems of ordinary differential equations; stability; finite differences for partial differential equations; Black–Scholes PDE connection overview.
Reading (book → chapters/sections): Boyce & DiPrima (selected) + Hull PDE sections + Shreve PDE sections (selected).
Coding deliverable: Implement finite-difference Black–Scholes pricer; compare to closed form; runtime and error analysis.
Time: 6–10 hrs
Module 3 — Stochastic Calculus and Numerical Methods: Stochastic Differential Equations, Partial Differential Equations, and Monte Carlo
Week 35: Stochastic Calculus: Brownian Motion, Quadratic Variation, and Path Properties
Topics: Brownian motion; increments; scaling; quadratic variation; simulation accuracy; path properties.
Reading (book → chapters/sections): Shreve Stochastic Calculus for Finance I (Brownian motion chapters).
Coding deliverable: Simulate Brownian paths; verify quadratic variation empirically; document discretization effects.
Time: 6–10 hrs
Week 36: Stochastic Calculus: Itô Integral, Itô Isometry, and Itô’s Lemma
Topics: Itô integral; Itô isometry; Itô’s lemma; applying Itô calculus to geometric Brownian motion and Ornstein–Uhlenbeck process.
Reading (book → chapters/sections): Øksendal Itô calculus chapters; Shreve Volume I Itô lemma sections.
Coding deliverable: Numerical verification of Itô’s lemma; compare time step sizes and discretization errors.
Time: 6–10 hrs
Week 37: Stochastic Differential Equations: Existence, Uniqueness, Geometric Brownian Motion, and Ornstein–Uhlenbeck Process
Topics: Existence/uniqueness; strong/weak solutions; exact vs numerical simulation; moments of OU; mean reversion.
Reading (book → chapters/sections): Øksendal stochastic differential equations chapters.
Coding deliverable: Implement Euler–Maruyama and exact OU simulation; compare moments; confidence intervals.
Time: 6–10 hrs
Week 38: Numerical Methods for Stochastic Differential Equations: Euler–Maruyama, Milstein, and Convergence Studies
Topics: Strong convergence; Milstein; discretization bias; step size studies; numerical stability.
Reading (book → chapters/sections): Kloeden & Platen numerical methods chapters (selected).
Coding deliverable: Compare Euler–Maruyama vs Milstein on GBM; strong error plots vs step size.
Time: 6–10 hrs
Week 39: Risk-Neutral Pricing: Change of Measure, Girsanov Theorem, and Likelihood Ratio Methods
Topics: Girsanov theorem; Radon–Nikodym derivative; risk-neutral measure; pricing via expectations.
Reading (book → chapters/sections): Shreve Stochastic Calculus for Finance II measure change chapters; Björk (selected).
Coding deliverable: Implement likelihood ratio drift change; price option under risk-neutral measure; unit tests.
Time: 6–10 hrs
Week 40: Monte Carlo Estimation of Greeks: Pathwise Derivatives, Likelihood Ratio Methods, and Bump-and-Reprice
Topics: Delta/vega estimators; pathwise derivatives; likelihood ratio estimators; bump-and-reprice bias/variance; smoothing overview.
Reading (book → chapters/sections): Glasserman Greeks chapter.
Coding deliverable: Implement delta via bump and pathwise; compare variance and bias; write short memo.
Time: 6–10 hrs
Week 41: Derivative Pricing via Partial Differential Equations: Finite Difference Methods for the Black–Scholes Equation
Topics: Black–Scholes PDE; boundary/terminal conditions; explicit/implicit schemes; stability; Greeks from PDE.
Reading (book → chapters/sections): Hull PDE sections; Shreve PDE chapters (selected).
Coding deliverable: Build finite difference pricer; compute delta/gamma; compare to Black–Scholes closed form.
Time: 6–10 hrs
Week 42: Stochastic Volatility Modeling: Heston Dynamics, Correlation, and Monte Carlo Pricing
Topics: Heston model dynamics; correlation; positivity issues; simulation schemes overview; effect on implied volatility smile.
Reading (book → chapters/sections): Gatheral Heston sections; Glasserman Monte Carlo sections.
Coding deliverable: Implement basic Heston simulation; Monte Carlo European pricing; sanity checks.
Time: 6–10 hrs
Week 43: Importance Sampling: Tail Estimation and Rare-Event Monte Carlo for Deep Out-of-the-Money Payoffs
Topics: Importance sampling; exponential tilting; rare-event estimation; estimator variance comparisons.
Reading (book → chapters/sections): Glasserman importance sampling sections.
Coding deliverable: Implement importance sampling for deep OTM option; compare estimator variance to standard Monte Carlo.
Time: 6–10 hrs
Week 44: Simulation and Model Risk: Discretization Bias, Parameter Uncertainty, and Stress Testing of Simulation Assumptions
Topics: Discretization bias; parameter uncertainty; stress testing; documentation of limitations; sensitivity analysis.
Reading (book → chapters/sections): McNeil QRM model risk sections (selected).
Coding deliverable: Write model risk checklist; apply to stochastic pricer; document mitigations and sensitivity results.
Time: 6–10 hrs
Week 45: Software Engineering for Quantitative Libraries: Application Programming Interface Design, Testing, Documentation, and Benchmarking
Topics: Library structure; packaging; documentation; unit tests; profiling; benchmarking; reproducibility.
Reading (book → chapters/sections): Clean Code + Kleppmann (selected).
Coding deliverable: Refactor earlier pricing/simulation code into a reusable package with tests, docs, and benchmarks.
Time: 6–10 hrs
Week 46: Monte Carlo Methods in Financial Engineering: Variance Reduction and Quasi-Monte Carlo Review
Topics: Variance reduction recap; quasi-Monte Carlo; error analysis; computational budgets; experiment design.
Reading (book → chapters/sections): Glasserman core chapters (selected).
Coding deliverable: Comparative study notebook: standard Monte Carlo vs control variate vs Sobol quasi-Monte Carlo for options.
Time: 6–10 hrs
Week 47: Ordinary Differential Equations: Systems, Stability, and Stiffness with Explicit and Implicit Methods
Topics: Systems of ODEs; stability; stiffness; explicit Runge–Kutta vs implicit Euler; stability regions.
Reading (book → chapters/sections): Boyce & DiPrima (selected); Strang computational ODE sections (optional).
Coding deliverable: Implement RK4 and implicit Euler; stiffness demo; stability plots.
Time: 6–10 hrs
Week 48: Boundary Value Problems for Ordinary Differential Equations: Shooting Methods and Finite Differences
Topics: Boundary value problems; shooting method; finite difference discretization; convergence and conditioning.
Reading (book → chapters/sections): Boyce & DiPrima boundary value problem sections.
Coding deliverable: Solve boundary value problem via shooting and finite differences; compare; convergence study.
Time: 6–10 hrs
Week 49: Partial Differential Equations: Classification and Elliptic Equations with Poisson Solvers
Topics: PDE classification; Poisson equation; sparse discretization; boundary conditions; convergence behavior.
Reading (book → chapters/sections): Strauss PDE (selected) + Strang computational PDE sections.
Coding deliverable: Sparse Poisson solver; error vs grid size; visualize solution.
Time: 6–10 hrs
Week 50: Partial Differential Equations: Heat Equation with Explicit and Implicit Schemes and Stability Analysis
Topics: Heat equation; FTCS; Crank–Nicolson; CFL stability; accuracy tradeoffs.
Reading (book → chapters/sections): Strauss heat equation sections + Strang.
Coding deliverable: Implement FTCS and Crank–Nicolson; stability experiments; error plots.
Time: 6–10 hrs
Week 51: Feynman–Kac Theorem: Connecting Stochastic Processes to Partial Differential Equations for Pricing
Topics: Feynman–Kac theorem; equivalence between PDE and expectation; consistency checks for models.
Reading (book → chapters/sections): Shreve Feynman–Kac sections; Glasserman (supporting).
Coding deliverable: Compare finite-difference vs Monte Carlo prices; error decomposition; runtime profiling.
Time: 6–10 hrs
Week 52: Numerical Integration and Quadrature Methods for Pricing and Risk: Gaussian Quadrature and Adaptive Schemes
Topics: Gaussian quadrature; adaptive quadrature; comparing quadrature vs Monte Carlo for smooth payoffs; error budgets.
Reading (book → chapters/sections): Strang numerical integration sections; Glasserman Ch 1–2 (supporting).
Coding deliverable: Implement Gaussian quadrature and adaptive quadrature; compare to Monte Carlo on pricing integrals.
Time: 6–10 hrs
Module 4 — Quantitative Finance: Fixed Income, Interest Rate Modeling (including Heath–Jarrow–Morton and LIBOR Market Model Calibration), Equity, Foreign Exchange, Inflation, Commodities, and Dependence
Week 53: Fixed Income Securities: Bond Pricing, Yield Conventions, Accrual, and Day Count Conventions
Topics: Bond cashflows; clean/dirty price; yield to maturity; compounding; day counts; accrued interest; numerical yield solving.
Reading (book → chapters/sections): Tuckman & Serrat Ch 1–3.
Coding deliverable: Implement bond pricer + yield solver with day-count conventions; unit tests and edge cases.
Time: 6–10 hrs
Week 54: Yield Curve Construction: Bootstrapping Discount Factors and Zero Rates from Bonds and Money Market Instruments
Topics: Bootstrapping discount factors; zero rates; interpolation choices; curve consistency; re-pricing checks.
Reading (book → chapters/sections): Tuckman curve chapters; Brigo & Mercurio curve construction sections.
Coding deliverable: Bootstrap a zero curve; compare interpolation methods; reprice instruments to validate.
Time: 6–10 hrs
Week 55: Interest Rate Swaps and Forward Rates: Pricing, Par Swap Rates, and Risk Measures such as DV01
Topics: Swap pricing; par swap rates; forward rates; discounting vs forwarding; DV01/PV01; key rate duration concept overview.
Reading (book → chapters/sections): Hull interest rate derivatives chapters; Tuckman swap chapters.
Coding deliverable: Implement swap pricer; compute DV01 and PV01 ladder; build portfolio risk report notebook.
Time: 6–10 hrs
Week 56: Multi-Curve Interest Rate Modeling: Overnight Indexed Swap Discounting, IBOR Forwarding, and Basis Spreads
Topics: OIS discounting; IBOR forwarding; basis spreads; valuation impacts; risk decomposition across curves.
Reading (book → chapters/sections): Brigo & Mercurio multi-curve introduction; Andersen & Piterbarg (selected).
Coding deliverable: Build toy OIS and IBOR curves; quantify basis impact on swap PV and DV01.
Time: 6–10 hrs
Week 57: Short-Rate Models: Vasicek and Hull–White Models with Affine Term Structure and Curve Calibration
Topics: Affine term structure; analytic zero-coupon bond pricing; Hull–White dynamics; calibration to initial curve; mean reversion effects.
Reading (book → chapters/sections): Brigo & Mercurio Hull–White/Vasicek chapters; Björk (rates sections optional).
Coding deliverable: Calibrate Hull–White to a curve; compare analytic vs Monte Carlo bond prices; sensitivity study.
Time: 6–10 hrs
Week 58: Short-Rate Models: Cox–Ingersoll–Ross Model, Positivity, and Parameter Calibration
Topics: CIR dynamics; positivity; analytical pricing; calibration; implications for tail behavior and volatility structure.
Reading (book → chapters/sections): Brigo & Mercurio CIR chapter.
Coding deliverable: Simulate CIR; calibrate to curve/moments; compare CIR vs Hull–White distributions and pricing effects.
Time: 6–10 hrs
Week 59: Caps and Floors: Black Model, Caplet Stripping, and Interest Rate Volatility Curves
Topics: Cap/floor valuation; Black caplet formula; caplet stripping; volatility term structures; day count conventions in practice.
Reading (book → chapters/sections): Hull caps/floors chapters; Brigo & Mercurio caplet sections (selected).
Coding deliverable: Implement caplet pricer; build synthetic caplet volatility curve; compute cap PV and risk metrics.
Time: 6–10 hrs
Week 60: Swaptions: Black Swaption Pricing, Swap Annuity, and Volatility Surface Construction
Topics: Swaption PV; swap annuity; Black swaption; building a grid of volatilities; sensitivities and greeks for interest rate options.
Reading (book → chapters/sections): Hull swaptions chapters; Brigo & Mercurio swaptions sections.
Coding deliverable: Implement swaption pricer; fit simple volatility surface; run sensitivity analysis and diagnostics plots.
Time: 6–10 hrs
Week 61: Heath–Jarrow–Morton Interest Rate Modeling: Drift Restriction, Forward Rate Dynamics, and Numerical Discretization
Topics: HJM setup; instantaneous forward rates; drift restriction; measures; discretization; stability issues and sanity checks.
Reading (book → chapters/sections): Brigo & Mercurio HJM chapters; Björk HJM chapter.
Coding deliverable: Implement one-factor HJM discretization; verify drift restriction numerically; compare simulated forwards to expectations.
Time: 6–10 hrs
Week 62: LIBOR Market Model Foundations: Lognormal LIBOR Dynamics, Measure Changes, and No-Arbitrage Structure
Topics: LMM setup; tenor structure; numeraire and measure changes; lognormal LIBOR; relationship to caplets and swaptions.
Reading (book → chapters/sections): Rebonato LMM introductory chapters; Brigo & Mercurio LMM sections.
Coding deliverable: Implement toy LMM simulation for several tenors; validate no-arbitrage identities; document assumptions.
Time: 6–10 hrs
Week 63: LIBOR Market Model Calibration for Caplets: Parametric Volatility Structures and Identifiability
Topics: Calibrating LMM to caplet volatilities; parametric volatility forms; identifiability; regularization and stability considerations.
Reading (book → chapters/sections): Rebonato calibration chapters.
Coding deliverable: Calibrate parametric LMM vol structure to synthetic caplet vols; report fit quality; parameter sensitivity.
Time: 6–10 hrs
Week 64: LIBOR Market Model Calibration for Swaptions: Correlation Structures, Smile Overview, and Model Risk
Topics: Swaption calibration; correlation matrix structures; smile introduction; SABR concept overview; model risk and diagnostics.
Reading (book → chapters/sections): Rebonato swaption calibration chapters; optional Hagan SABR paper.
Coding deliverable: Extend calibration to swaption vols; incorporate correlation; diagnostics and model risk notes.
Time: 6–10 hrs
Week 65: Interest Rate Smile Modeling: SABR Approximation, Calibration, and Diagnostic Checks
Topics: SABR parameters; implied volatility approximation; calibration stability; diagnostics; limitations and practical choices.
Reading (book → chapters/sections): Rebonato smile chapters; Hagan SABR paper (optional).
Coding deliverable: Implement SABR implied vol; calibrate to synthetic smile; diagnostic plots; parameter stability study.
Time: 6–10 hrs
Week 66: Yield Curve Risk Simulation: Principal Component Analysis Shocks, Historical Scenarios, and Stress Testing
Topics: PCA of yield curve changes; scenario generation; full revaluation vs delta approximations; stress testing design.
Reading (book → chapters/sections): Tuckman risk chapters; McNeil QRM stress testing sections (selected).
Coding deliverable: Generate PCA shocks; compute portfolio P&L; distribution; compare delta-normal vs full revaluation on toy portfolio.
Time: 6–10 hrs
Week 67: Equity Return Modeling: Stylized Facts, Heavy Tails, and Distribution Fitting for Risk Measurement
Topics: Log returns; volatility clustering overview; heavy tails; skewness/kurtosis; fitting Normal vs Student-t; tail risk implications.
Reading (book → chapters/sections): Cochrane (selected) + McNeil QRM tail risk sections.
Coding deliverable: Fit Normal vs Student-t; compare Value-at-Risk and Expected Shortfall; diagnostics and reporting.
Time: 6–10 hrs
Week 68: Equity Factor Modeling: Capital Asset Pricing Model and Multifactor Regressions with Robustness Checks
Topics: CAPM; multifactor (Fama–French); regression estimation; rolling betas; robustness and regime sensitivity.
Reading (book → chapters/sections): Cochrane factor chapters; Fama–French papers (selected).
Coding deliverable: Build multifactor regressions; rolling analysis; factor attribution report notebook.
Time: 6–10 hrs
Week 69: Equity Derivatives Pricing: Binomial Lattices, Replication, and Convergence to Black–Scholes
Topics: Replication; binomial pricing; convergence; greeks estimation; discretization tradeoffs.
Reading (book → chapters/sections): Hull binomial chapters.
Coding deliverable: Implement CRR tree; compare to Black–Scholes; convergence study; unit tests.
Time: 6–10 hrs
Week 70: Volatility Surface Modeling: Implied Volatility Smiles and Parameterizations such as Stochastic Volatility Inspired and SVI
Topics: Smiles and surfaces; static arbitrage considerations (overview); SVI parameterization; diagnostic checks.
Reading (book → chapters/sections): Gatheral volatility surface chapters.
Coding deliverable: Fit SVI to synthetic implied volatility surface; heuristic arbitrage checks; visualization dashboard.
Time: 6–10 hrs
Week 71: Local Volatility Modeling: Dupire Calibration Concepts and Numerical Pricing Implications
Topics: Dupire local volatility; calibration pipeline; local vs stochastic volatility; numerical issues in PDE and Monte Carlo pricing.
Reading (book → chapters/sections): Gatheral local volatility sections.
Coding deliverable: Toy local volatility calibration; price Europeans across strikes; compare to Black–Scholes and implied vols.
Time: 6–10 hrs
Week 72: Stochastic Volatility Calibration Workflow: Heston Model Parameter Sensitivities and Practical Limitations
Topics: Heston parameter effects on smile; calibration workflow; identifiability; numerical stability; model risk notes.
Reading (book → chapters/sections): Gatheral Heston chapters (selected).
Coding deliverable: Calibrate rough Heston parameters to synthetic smile; compare fit; document limitations and sensitivities.
Time: 6–10 hrs
Week 73: Foreign Exchange Forwards and Interest Rate Parity: Pricing and Numeraire Considerations
Topics: FX quoting; spot and forward; covered interest parity; basic numeraire change intuition; curve dependence of FX forwards.
Reading (book → chapters/sections): Clark FX introductory chapters; Björk numeraire sections (optional).
Coding deliverable: Build FX forward pricer; parity checks; sensitivity to interest rate curves.
Time: 6–10 hrs
Week 74: Foreign Exchange Options: Delta Conventions, Risk Reversals, Butterflies, and Smile Construction from Market Quotes
Topics: Delta conventions; risk reversals; butterflies; constructing smile; practical risk metrics and quoting nuances.
Reading (book → chapters/sections): Clark FX smile chapters.
Coding deliverable: Build FX smile from synthetic RR/BF quotes; compute implied vols across deltas; plot and diagnose smile.
Time: 6–10 hrs
Week 75: Cross-Currency Basis and Cross-Currency Swaps: Multi-Curve and Foreign Exchange Interaction
Topics: Cross-currency swaps; basis; discounting/forwarding across currencies; valuation and risk impacts.
Reading (book → chapters/sections): Andersen & Piterbarg (selected) + Brigo & Mercurio multi-curve sections.
Coding deliverable: Toy cross-currency swap PV with basis; sensitivity study; clear documentation.
Time: 6–10 hrs
Week 76: Inflation-Linked Products: Inflation Curves, Zero-Coupon Inflation Swaps, and Seasonality
Topics: Inflation indices; building inflation curves; zero-coupon inflation swaps; seasonality adjustments (overview); real vs nominal measures concept (overview).
Reading (book → chapters/sections): Mercurio inflation-linked products (selected).
Coding deliverable: Price a zero-coupon inflation swap (toy); build inflation curve from synthetic quotes; seasonality demonstration.
Time: 6–10 hrs
Week 77: Commodity Modeling Basics: Convenience Yield, Mean Reversion, and Futures Curve Dynamics
Topics: Commodity spot vs futures; convenience yield; mean reversion; term structure behavior; storage costs overview.
Reading (book → chapters/sections): Carmona commodity modeling (selected) or Eydeland & Wolyniec (selected).
Coding deliverable: Implement mean-reverting commodity spot model; derive toy futures curve; simulate curve scenarios.
Time: 6–10 hrs
Week 78: Multi-Asset Dependence Modeling: Correlation, Copulas, Tail Dependence, and Regime Intuition
Topics: Correlation limitations; Gaussian vs t-copulas; tail dependence; regime intuition; impacts on joint tail risk and capital.
Reading (book → chapters/sections): McNeil QRM copula chapters.
Coding deliverable: Simulate joint returns with t-copula vs Gaussian; compare joint tail metrics; narrative interpretation.
Time: 6–10 hrs
Week 79: Risk Forecasting and Backtesting: Value-at-Risk, Expected Shortfall, and Forecast Evaluation Methods
Topics: Value-at-Risk vs Expected Shortfall; backtesting ideas; exception analysis; forecast evaluation; model drift monitoring.
Reading (book → chapters/sections): McNeil QRM risk measure and backtesting chapters.
Coding deliverable: Implement VaR/ES backtesting for a multi-asset portfolio; exception report and plots.
Time: 6–10 hrs
Week 80: Model Governance and Validation in Quantitative Finance: Sensitivity, Stress Testing, and Documentation Standards
Topics: Validation practices; sensitivity analysis; stress testing; documentation; model risk management; reproducibility standards.
Reading (book → chapters/sections): McNeil QRM model risk sections (selected) + Clean Code/Kleppmann (supporting).
Coding deliverable: Create a validation pack for one rates or equity model; automate checks; produce concise validation memo.
Time: 6–10 hrs
Module 5 — Quantitative Finance Advanced: Credit Risk, Counterparty Risk (XVA), Forecasting, Machine Learning, and Integrated Capstones
Week 81: Credit Risk Modeling: Hazard Rates, Recovery, Credit Spreads, and Risky Bond Pricing Foundations
Topics: Credit spreads; hazard rates; recovery; risky discounting; pricing risky zero-coupon bonds and credit risky cashflows.
Reading (book → chapters/sections): Lando Ch 1–2; Duffie & Singleton introduction.
Coding deliverable: Build spread-to-hazard calculator; price a risky bond (toy); unit tests.
Time: 6–10 hrs
Week 82: Structural Credit Risk Modeling: Merton Model, Distance-to-Default, and Equity-to-Credit Links
Topics: Merton model; firm value dynamics; default barrier; distance-to-default; sensitivity to leverage and asset volatility.
Reading (book → chapters/sections): Lando structural credit chapter.
Coding deliverable: Implement Merton probability of default estimator; stress leverage/volatility; compare to spread-implied probability of default.
Time: 6–10 hrs
Week 83: Reduced-Form Credit Risk Modeling: Survival Curve Bootstrapping from Credit Default Swap Spreads
Topics: Reduced-form intensity; survival probabilities; bootstrapping hazard curve from credit default swaps; credit default swap present value mechanics.
Reading (book → chapters/sections): Lando intensity chapters; O’Kane (selected chapters).
Coding deliverable: Bootstrap survival curve from synthetic credit default swap spreads; compute credit default swap PV; unit tests.
Time: 6–10 hrs
Week 84: Stochastic Intensity Models: Affine Intensities, Simulation of Default Times, and Calibration Concepts
Topics: Stochastic intensity processes; affine specifications; simulation of default times; calibration considerations; Monte Carlo pricing.
Reading (book → chapters/sections): Duffie & Singleton intensity chapters; Lando stochastic intensity sections.
Coding deliverable: Simulate Cox–Ingersoll–Ross intensity; generate default times; toy credit default swap pricing by Monte Carlo; diagnostics.
Time: 6–10 hrs
Week 85: Counterparty Exposure Simulation: Expected Exposure, Potential Future Exposure, and Netting and Collateral Concepts
Topics: Exposure profiles; expected exposure; potential future exposure; netting sets; collateral and credit support annex concepts.
Reading (book → chapters/sections): Gregory exposure chapters; Brigo/Morini/Pallavicini (selected).
Coding deliverable: Simulate swap exposure under Hull–White rates; produce expected exposure and potential future exposure profiles; documentation.
Time: 6–10 hrs
Week 86: Valuation Adjustments: Credit Valuation Adjustment, Debit Valuation Adjustment, and Funding Valuation Adjustment
Topics: Unilateral and bilateral credit valuation adjustment; debit valuation adjustment; funding valuation adjustment overview; inputs and sensitivities.
Reading (book → chapters/sections): Gregory XVA chapters; Brigo/Morini/Pallavicini.
Coding deliverable: Compute simplified credit valuation adjustment for a swap using hazard curve and expected exposure; extend to toy debit/funding adjustments; sensitivity analysis.
Time: 6–10 hrs
Week 87: Wrong-Way Risk Modeling: Dependence between Exposure and Default using Copulas and Stress Scenarios
Topics: Wrong-way risk; dependence between exposure and default; copula approaches; stress testing; governance considerations.
Reading (book → chapters/sections): Brigo/Morini/Pallavicini wrong-way risk sections + McNeil QRM copulas.
Coding deliverable: Implement copula-based wrong-way risk: correlate hazard with rates; compare credit valuation adjustment with/without wrong-way risk.
Time: 6–10 hrs
Week 88: Credit Portfolio Modeling and Tranche Losses: One-Factor Copula Models and Tail Dependence
Topics: One-factor portfolio models; Gaussian vs t-copula; tranche expected losses; tail dependence impacts; model risk in correlation assumptions.
Reading (book → chapters/sections): McNeil QRM copulas and credit portfolio sections.
Coding deliverable: Simulate portfolio loss distribution; compute tranche expected loss; compare Gaussian vs t-copula tails; commentary memo.
Time: 6–10 hrs
Week 89: Time Series Risk Forecasting: Exponentially Weighted Moving Average and Generalized Autoregressive Conditional Heteroskedasticity Models
Topics: Volatility forecasting; EWMA; GARCH; forecast evaluation; backtesting Value-at-Risk; regime intuition overview.
Reading (book → chapters/sections): Tsay financial time series (selected) + McNeil QRM forecasting/backtesting sections.
Coding deliverable: Build EWMA and GARCH volatility forecasts; VaR backtest; exception report.
Time: 6–10 hrs
Week 90: Machine Learning for Pricing and Risk: Gradient Boosting and Surrogate Modeling for Fast Approximation
Topics: Surrogate modeling; gradient boosting; calibration-as-optimization; train/validation splits; leakage pitfalls; error analysis.
Reading (book → chapters/sections): ISLR/ESL (selected) + practical notes.
Coding deliverable: Train surrogate pricer for option prices; compare speed vs baseline; error diagnostics and confidence bounds.
Time: 6–10 hrs
Week 91: Deep Hedging Overview: Policy-Based Hedging, Evaluation Metrics, and Practical Implementation Constraints
Topics: Policy-based hedging; objective functions; constraints; evaluation vs delta hedging; practical considerations and failure modes.
Reading (book → chapters/sections): Selected deep hedging papers (Buehler et al.) + Glasserman critique notes.
Coding deliverable: Implement toy neural-network hedge vs delta hedge under GBM; compare hedging P&L; distribution.
Time: 6–10 hrs
Week 92: Production Engineering for Quantitative Systems: Packaging, Continuous Integration, Versioned Data, and Reproducible Pipelines
Topics: Production practices; packaging; CI; versioned datasets; reproducible pipelines; logging; monitoring; model governance integration.
Reading (book → chapters/sections): Clean Code + Kleppmann + pytest documentation.
Coding deliverable: Refactor one project into production layout; add CI, tests, docs, and benchmark script.
Time: 6–10 hrs
Week 93: Capstone Integration: Production-Quality Interest Rate Modeling and Derivatives Analytics Library
Topics: Unify curves (OIS/IBOR), swaps, caps/floors, swaptions, Hull–White/CIR simulation, PCA shocks, calibration notebooks.
Reading (book → chapters/sections): Tuckman + Brigo & Mercurio + Rebonato + Glasserman (as used earlier).
Coding deliverable: Deliver rates library with tests and CI, calibration notebook, and risk report.
Time: 8–12 hrs
Week 94: Capstone Integration: Production-Quality Credit Risk and Counterparty Risk (XVA) Analytics Engine
Topics: Survival bootstrap; credit default swap pricer; exposure simulation; credit valuation adjustment/debit/funding adjustments; wrong-way risk toggles; credit portfolio loss and tranche expected loss.
Reading (book → chapters/sections): Lando + Duffie/Singleton + Gregory + Brigo/Morini/Pallavicini + McNeil QRM.
Coding deliverable: Deliver credit/XVA engine with tests and CI and exposure/valuation adjustment dashboards (notebook).
Time: 8–12 hrs
Week 95: Capstone Integration: Integrated Asset-Liability Management Engine with Asset Models and Liability Cashflow Projection
Topics: Integrate simulated rates, equity, and credit with liability cashflow projection; compute net asset value/surplus distributions; Value-at-Risk/Conditional Tail Expectation; stress scenarios.
Reading (book → chapters/sections): Glasserman + McNeil QRM + Tuckman; life contingency cashflow references (supporting).
Coding deliverable: Deliver integrated asset-liability management engine meta-repository; run scenario studies; produce executive risk narrative.
Time: 8–12 hrs
Week 96: Capstone Integration: Portfolio Packaging, Technical Report, Executive Slide Deck, and Demonstration Walkthrough
Topics: Polish repositories; unify style; add CI badges; write 15–25 page report; produce 12-slide deck; demo script and resume bullets.
Reading (book → chapters/sections): Clean Code + Kleppmann + communication checklist.
Coding deliverable: Deliver final portfolio: 3–4 repositories, long report, slides, and demo plan.
Time: 8–12 hrs
Module 6 — Actuarial Modeling: Loss Models, Reserving, Credibility, Reinsurance, Life Contingencies, Insurance Capital, and Integrated Capstones
Week 97: Actuarial Loss Modeling: Frequency Distributions, Severity Distributions, Estimation, and Diagnostics
Topics: Claim count models (Poisson, Negative Binomial, zero-inflation overview); severity models (Gamma, Lognormal, Weibull, Pareto); estimation; goodness-of-fit; truncation/censoring overview.
Reading (book → chapters/sections): Klugman, Panjer, Willmot — Loss Models (frequency and severity chapters); Frees et al. predictive modeling (distribution fitting sections).
Coding deliverable: Fit frequency and severity models to synthetic claims; compare AIC/BIC; diagnostics; reusable fitting utilities.
Time: 6–10 hrs
Week 98: Aggregate Loss Modeling: Compound Distributions, Panjer Recursion, Fast Fourier Transform Methods, and Simulation
Topics: Compound sum distributions; Panjer recursion; discretization; FFT convolution overview; Monte Carlo aggregation; accuracy/runtime tradeoffs.
Reading (book → chapters/sections): Loss Models aggregate chapters; Wüthrich & Merz (supporting).
Coding deliverable: Implement Panjer recursion and Monte Carlo aggregate loss; optional FFT convolution; compare accuracy and runtime.
Time: 6–10 hrs
Week 99: Tail Risk and Extreme Value Theory for Insurance Losses: Generalized Pareto Distribution, Threshold Selection, and Expected Shortfall
Topics: Extreme value theory; peaks-over-threshold; generalized Pareto distribution; threshold diagnostics; Value-at-Risk and Conditional Tail Expectation sensitivity; tail model risk.
Reading (book → chapters/sections): McNeil QRM EVT chapters; Loss Models tail sections.
Coding deliverable: Fit generalized Pareto distribution to synthetic tail losses; threshold diagnostics; compute VaR/CTE; sensitivity analysis.
Time: 6–10 hrs
Week 100: Credibility Theory: Bühlmann Credibility, Bühlmann–Straub Model, and Bayesian Interpretation
Topics: Credibility premium derivation; Bühlmann model; Bühlmann–Straub; Bayesian interpretation; applications to pricing/experience studies.
Reading (book → chapters/sections): Bühlmann & Gisler credibility chapters; Loss Models credibility sections.
Coding deliverable: Implement Bühlmann and Bühlmann–Straub estimators; apply to grouped risks; sensitivity analysis.
Time: 6–10 hrs
Week 101: Reinsurance Modeling: Quota Share, Excess of Loss, Stop Loss, and Capital Impact of Risk Transfer
Topics: Reinsurance treaty structures; ceded vs net loss distributions; attachment/limit; reinstatements overview; impact on VaR/CTE and capital; pricing intuition.
Reading (book → chapters/sections): Loss Models reinsurance chapters; McNeil QRM risk measures (supporting).
Coding deliverable: Simulate gross vs net losses under multiple treaties; compute VaR/CTE reduction; cost-benefit report.
Time: 6–10 hrs
Week 102: Stochastic Reserving Methods: Chain Ladder, Mack Model Variance, and Claims Development Triangles
Topics: Run-off triangles; chain ladder; development factors; Mack model variance; assumptions/diagnostics; process vs parameter risk overview.
Reading (book → chapters/sections): Wüthrich & Merz stochastic reserving chapters; Mack chain ladder paper; England & Verrall (optional).
Coding deliverable: Implement chain ladder and Mack variance on synthetic triangle; reserve uncertainty report and diagnostics plots.
Time: 6–10 hrs
Week 103: Generalized Linear Models for Reserving and Claims Modeling: Overdispersion, Calendar Effects, and Model Selection
Topics: Generalized linear model reserving; Poisson/Gamma models; overdispersion; calendar effects; model selection; residual diagnostics.
Reading (book → chapters/sections): Wüthrich & Merz generalized linear model reserving sections; Frees et al. predictive modeling chapters.
Coding deliverable: Build GLM reserving model on synthetic triangle; compare to chain ladder; residual analysis and model comparison.
Time: 6–10 hrs
Week 104: Experience Studies for Life Insurance: Mortality, Lapse, and Expense Assumption Setting with Cohort Methods
Topics: Exposure calculation; crude rates; smoothing/graduation overview; mortality improvement concepts; lapse modeling; governance and documentation.
Reading (book → chapters/sections): Dickson, Hardy & Waters (selected) + actuarial practice notes; Frees (optional for lapse modeling).
Coding deliverable: Create synthetic cohort data; compute mortality/lapse rates; smoothing demo; assumption memo template.
Time: 6–10 hrs
Week 105: Life Contingencies and Product Cashflow Modeling: Present Value, Survival Models, and Annuity and Life Insurance Cashflows
Topics: Survival functions; life tables; present values of benefits/premiums; life annuities; term insurance; net premium reserves; projection engine linkage.
Reading (book → chapters/sections): Bowers et al. life contingencies chapters; Dickson, Hardy & Waters (selected).
Coding deliverable: Implement life contingency cashflow engine for term life and life annuity; validate against closed-form PV in simple cases.
Time: 6–10 hrs
Week 106: Policyholder Behavior Modeling: Dynamic Lapse, Surrender, and Utilization Models with State Dependence
Topics: State-dependent behavior; moneyness; interest rate effects; logistic/GLM approaches; hazard models; impacts on reserves and hedging.
Reading (book → chapters/sections): Frees predictive modeling; selected notes/papers on dynamic lapse (optional).
Coding deliverable: Simulate behavior models (logistic/hazard); stress scenarios; quantify reserve sensitivity.
Time: 6–10 hrs
Week 107: Insurance Reporting and Capital Frameworks: Statutory versus Economic Views, Risk-Based Capital Concepts, and IFRS 17 Overview
Topics: Statutory vs economic valuation; discount rates; margin concepts; risk-based capital components; IFRS 17 building blocks overview; governance implications.
Reading (book → chapters/sections): Practice-oriented references (society notes) + McNeil QRM capital context.
Coding deliverable: Create statutory vs economic comparison memo template; implement toy capital calculation from simulated distributions.
Time: 6–10 hrs
Week 108: Insurance Asset-Liability Management: Liability Duration, Key Rate Duration, Surplus Sensitivities, and Hedging Objectives
Topics: Liability duration/convexity; key rate duration for liability cashflows; surplus sensitivity; hedging objectives; rebalancing rules.
Reading (book → chapters/sections): Tuckman hedging chapters + actuarial ALM notes; McNeil QRM (supporting).
Coding deliverable: Compute liability duration and key rate durations from cashflow engine; design a simple hedging portfolio; surplus sensitivity report.
Time: 6–10 hrs
Week 109: Actuarial Pricing Frameworks: Indicated Rate Level, Risk Loads, Profit Testing, and Sensitivity Analysis
Topics: Pricing components; risk loads; profit testing; capital charges; sensitivity to assumptions; governance and documentation.
Reading (book → chapters/sections): Loss Models pricing context + actuarial pricing practice references; Frees predictive modeling (pricing features).
Coding deliverable: Build simplified pricing model in Python: indicated rate equals expected loss + expense + profit + capital load; sensitivity study.
Time: 6–10 hrs
Week 110: Integrated Actuarial Capstone: Insurance Loss Model to Capital Model Pipeline with Reinsurance and Dependence
Topics: End-to-end pipeline: fit frequency/severity; aggregate loss; reinsurance; dependence via copulas; capital (VaR/CTE); reporting; model risk notes.
Reading (book → chapters/sections): Loss Models + McNeil QRM + Bühlmann credibility theory.
Coding deliverable: Deliver loss-to-capital pipeline notebook with reusable functions and reproducible results.
Time: 8–12 hrs
Week 111: Integrated Actuarial and Quantitative Finance Capstone: Economic Scenario Generator Linking Rates, Equity, Credit, and Insurance Risks
Topics: Integrate simulated rates/equity/credit with insurance cashflows; compute surplus distribution; include credit spreads/default; stress tests and scenario narratives.
Reading (book → chapters/sections): Brigo & Mercurio + Lando/Gregory + Loss Models + McNeil QRM.
Coding deliverable: Extend ALM engine to include credit spread/default module and insurance loss module; produce stress scenario report.
Time: 8–12 hrs
Week 112: Final Portfolio Consolidation for Actuarial Quant Roles: Reports, Presentations, Documentation, and Interview-Ready Narrative
Topics: Finalize documentation across actuarial and finance components; unify style; ensure tests and CI; produce master report and executive deck; demo plan.
Reading (book → chapters/sections): Clean Code + Kleppmann + communication checklist.
Coding deliverable: Deliver master portfolio package: actuarial loss/capital repository + integrated ALM repository + final report + slide deck + demo plan.
Time: 8–12 hrs
Conic Sections in MPT
It All Begins Here
I was tutoring a student about the general geometry of conic sections (circles, parabolas, ellipses and hyperbolas) and was wondering if this can be applied in an actuarial or quantitative framework. According to ChatGPT, it can. Modern portfolio theory (MPT) states that the return (mu) relative to the risk (sigma) can be plotted in the form of a hyperbola/parabola (parabola if plotted against the variance of the portfolio). ChatGPT also states that two highly correlated assets can be modeled as an ellipse. I found this interesting because if that’s true, how can I use the property of conic sections to maximize the performance of a portfolio? If the utility/budget constraints can be modeled as a straight line, can I use the properties of general geometry to maximize return and minimize risk?