Teaching

Two financial-engineering courses taught most recently at the University of Illinois during the academic year of 2013-2014, for the Master of Science in Financial Engineering (MSFE), a joint program of the Colleges of Business and Engineering.

Spring, 2014 and Fall, 2013: Both honored in the “Lists of Teachers Ranked as Excellent” by the University.

Spring Semester, 2014 (Completed) -- IE 525:

Computation in Finance.

Course Description:

Numerical methods for the modeling, pricing, and risk management of various financial instruments and services, including in particular derivatives: (STOCHASTIC) randomization and anti-gaming, Monte Carlo simulation, variance reduction techniques, quasi Monte Carlo methods; (DETERMINISTIC) finite difference methods for ordinary and partial differential equations, explicit and implicit schemes, boundary conditions, and free boundary problems for American options; (DATA ANALYTICAL) data-driven model calibration and optimization, financial data pattern analysis and synthesis, filtering and machine learning, analytics in high-frequency data environment.

Syllabus in PDF.

Problem Set 1: Numerical Integration (N.I.), Error Analysis, RNG, Central Limit Theorem, Derivative Pricing via N.I. or Monte-Carlo.
Problem Set 2: Box-Muller Algo, Rejection-Acceptance Algo, Knuth Algo, Event Timing and Counts (e.g. for Credit or Insurance).
Problem Set 3: (Monte-Carlo) Antithetic Noise Cancellation, Stratification and Adaptive Sampling, Faithful Path Simulation (LogNormal, Vasicek Mean-Reversal), Pricing of European/Asian Calls or Puts, Path-Dependent Interest Rate Options (Range Accrual)
Problem Set 4: Correlation Mining; Cholesky Decomposition; Correlated Dynamics; Exchange Options; Multiple Assets
*** Midterm Events: Review Lecture on Mon, March 10; Formal Exam on Wed, March 12
*** One-Week Spring Break: Have a Safe and Joyful Spring Break !
Problem Set 5: (Brief due to Spring Break) Explicit/Implicit Schemes; Data Noise and Stability; Heat Equations, Black-Scholes
Problem Set 6: Optimal Design of Grids and Boundaries; Scheme Stability; Calls/Puts; Numerical Greeks; Barrier Options
Problem Set 7: Free-Boundary Black-Scholes PDE, American Puts; (Data Analytics) Model Calib via MLE; Kullback-Leibler Distance
Lecture Notes (Last): (Data Analytics) Gaussian Mixtures; Hidden States; EM Algorithm; Membership’s

Fall Semester, 2013 (Completed) -- IE 524:

Optimization in Finance.

Syllabus in PDF.

2013/08/26: PS 1 (Warming Up on Finance, Linear Algebra, and Calculus).
2013/09/04: PS 2 (Financial LPs and MATLAB linprog(…); Brief due to Labor Day).
2013/09/09: PS 3 (LP: Physics, Geometry; Local Affine Coordinates; Generics).
2013/09/16: PS 4 (LP: Simplex Method; Tableau Computation; Duality). Duality Flowchart.
2013/09/23: PS 5 (NLP: Bisection/Newton; KKT Conditions; Convexity; Implied Volatilities).
2013/10/04: PS 6 (QP: Lagrangians; Duality of QP; Optimal Portfolio Construction).
*** Midterm Events: Review Lecture on Wed, Oct. 9; Formal Exam on Mon, Oct. 14.
2013/10/16: Project (Index Tracking: Small/Large Cap, Liquidity, Tracking Error, Constrained QP).
2013/10/23: PS 7 (Efficient Frontiers; Trans. Costs; Sharpe Ratios; Transform Methods (to QP)).
*** Group Project Presentations (9 Teams) on Wed, Nov. 13 and Mon, Nov. 18.
*** One-Week Thanksgiving Break: Happy Thanksgiving !
2013/12/02: PS 8 (DP; State/Control Vars; State Eqn’s; Bellman Eqn’s; Algorithmic Trading).

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