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APS 1022 Financial Engineering II

Prerequisite: APS 1002 or equivalent, multi-variate calculus, probability and statistics, MATLAB programming or equivalent.

Required: Investment Science by David Luenberger (first or second edition)

Course is in two parts: 

Part 1 Advanced Portfolio Optimization May 12-16 (Course Instructor:Roy H. Kwon, [email protected])

Major Topics:

(1) Mean-Variance Optimization (MVO): MVO with and without short selling, alternative forms of MVO, practical issues in large-scale applications (overconcentration, complexity of parameter estimation, transaction costs (turnover constraints)), factor-model approach (single and multi-factor), mean absolute deviation linear programming equivalent to MVO. Black-Litterman Portfolio Optimization

(2) Quadratic Optimization (aka quadratic programming QP): MVO as a QP, MVO requirements( positive-semi definite and positive definite covariance matrices), general non-linear optimization theory: unconstrained and unconstrained optimality conditions, KKT conditions for QP and MVO. Convex optimization.

(3) Discrete Choice in Portfolio Optimization: MVO with cardinality constraints and Index Tracking.

(4) Portfolio Optimization under uncertainty: maximum expected utility portfolio optimization, stochastic programming, robust optimization, CVaR optimization. Exam May 16 from 1-4PM 80% of Part 1 Marks (Exam will be held in BA 2185 from 1-4PM, you will be allowed two sides of a 3 by 5 inch note card, otherwise exam is closed book and closed notes, a non-programmable and non-financial calculator is permitted)Computational Projects 20% of Park 1 Marks Details (will be due after the 23rd of May other specific due date TBD) First project must be done individually and the second will a group (you can form a group of 2-3 students).

Note: Total Marks from Part 1 is 50% of overall course mark.

Part 2: Derivative Securities and Pricing

Instructor: Prof: Chi-Guhn Lee, [email protected]

Office: MC322 (416-946-7867)

Textbook and Reading

Required: Investment Science by David Luenberger (first or second edition)

(1) Asset dynamics, lattice and Monte Carlo simulation Stochastic processes to model asset price dynamics such as Markov process, wiener process and geometric Brownian motion. As a computational tool, lattice and Monte Carlo simulation will be discussed.

(2) Derivatives: forwards, futures, options and swaps Basic derivatives, such as forwards, futures, options, and swaps, are introduced along with their pricing methods. Also covered is hedging (the

perfect hedging and the minimum-variance hedging) using derivatives.

(3) Option theory Options will be discussed in more detail including types of option, put-call parity, risk-neutral valuation, the Black-Scholes formula, and exotic options.

a. Exam will be held in class on the last day of the second week

b. You will be allowed two sides of a letter paper

c. Otherwise, exam is closed book and closed notes, a nonprogrammable and non-financial calculator is permitted

(2) Computational Project (20%)

a. Derivative pricing using lattice and Monte Carlo simulation

b. Group project

c. Final report with less than 20 pages (excluding appendix)