I graduated from the Master of Quantitative Finance program at the Swiss Federal Institute of Technology (ETH Zurich).
The topic of my master thesis was: "Trend and Mean Reversion Modelling in a Market with Heterogeneous Investors: A Dynamical Systems Approach".
Below you can see a list of brief descriptions of the graduate courses that I have taken:
Mathematical Foundations of Finance
First introduction to main ideas and tools from mathematical finance, Financial market models in finite discrete time, Absence of arbitrage and martingale measures measures Valuation , Valuation and and hedging in complete hedging in complete markets markets, Basics about Brownian motion, Stochastic integration, Stochastic calculus: Ito formula, Girsanov transformation, Ito's representation theorem, theorem, Black Black-Scholes formula
Cash Flow Engineering and Forward Contracts, Interest Rate Derivatives, Swap Engineering, Exchange Traded Funds, Mechhanics of Options, Option Greeks and and Their Uses, Engineering Convexity Positions, Profit & Loss, Credit Derivatives
Continuous Time Quantitative Finance
– American Options
– Stochastic Volatility
– Lévy Processes and Option Pricing
– Exotic Options
– Real Options
– Environmental Finance
Asset Management Advanced Investments
– Traditional portfolio construction (Markowitz optimization, CAPM, and APT within a multi-asset framework)
– Practical problems of the traditional portfolio theory and solutions such as resampling and robust portfolio optimization
– Bayesian approaches to portfolio optimization
– Black-Litterman model and its extensions
– Dynamic optimization approach, regime switches in discrete time and continuous continuous time approaches time approaches
Computational Methods in Quantitative Finance: PDE Methods
Review of option pricing. Wiener and Levy price process models. Deterministic, local and stochastic volatility models. Finite difference methods for option pricing. Relation to bi- and multinomial trees, European contracts. Finite Difference methods for Asian, American and Barrier type contracts. Finite element methods for European and American American style style contracts contracts Pricing. Pricing under under local and stochastic volatility in local and stochastic volatility in Black-Scholes Markets. Finite Element Methods for option pricing under Levy processes. Treatment of integrodifferential operators. Stochastic volatility models for Levy processes. Techniques for multidimensional problems. Baskets in a Black-Scholes setting and stochastic volatility models in Black Scholes and Levy markets. Introduction to sparse grid techniques.
Computational Methods in Quantitative Finance: Monte Carlo and Sampling Methods
Course on numerical solution of stochastic (Ito) differential equations, with emphasis on general, multiplicative diffusions, possibly degenerated. Mathematical Analysis of solution methods, applications to quantitative finance as well as to sciences are considered. Generalizations to diffusions with jumps and Levy noise are outlined.
Basic Monte-Carlo (MC) Techniques: Random Number Generators, MC for a scalar random variable (RV): Implementation and error estimation.
MC for stochastic processes: Markov Processes: Wiener, Poisson, Compound Poisson, Levy Processes (single and multivariate), Path regularity of processes. Simulation and MC for stochastic processes. Application to pricing of basic financial contracts (call, put, european, american, asian), on single underlying and baskets, Error analysis and computer implementation.
Application to Computational Finance: Option Pricing: Black Scholes (BS) Market Model, No arbitrage principle, Changes of Measure. Basic types of derivative contracts: plain vanilla, barrier, Europeans, Asians. Incomplete markets and equivalent martingale measures.
Existence, Uniqueness of weak and strong solutions of Ito-Stochastic Differential Equations. Yamada-type degeneracies. Numerical solution: Euler-Maruyama, Milstein and higher order schemes, weak, strong and pathwise convergence. Applications: MC based Option Pricing in Black-Scholes Setting. Stochastic Volatility Models. Heston and Chemical Master Equation.
Jump Diffusions and Levy Driven Stochastic Differential Equations, Theory of Levy Stochastic Differential Equations: Existence, Path regularity, Numerical solution: fast increment generation, Euler-Maruyama, extrapolation, Applications: MC based Option Pricing in Incomplete Markets.
Convergence Acceleration for MC: Variance Reduction, Extrapolation Techniques Quasi MC, Adaptive Sampling Methods, MLMC.
Economic Foundations of Finance
– Basics from game theory and general equilibrium theory which are the two main foundations for financial theory
Advanced Financial Economics
Portfolio Theory, CAPM, Financial Derivatives, Incomplete Markets, Corporate Finance, Behavioural Finance, Evolutionary Finance, Asymmetric Asymmetric Information Information
Advanced Corporate Finance 1
Net present value, Valuation under uncertainty, Capital structure: Perfect markets and irrelevance, Leverage and the cost of capital, Leverage and financial ratios ratios Payout , Payout policy: policy: Dividends and share Dividends and share repurchases repurchases Capital, Capital structure: Taxes and bankruptcy costs, Capital structure: Information asymmetries and agency costs, Valuation: Adjusted present value and WACC
Advanced Corporate Finance 2
The role of information and incentives in determining the forms of financing a firm chooses; hedging; venture capital; initial public offerings; investment in very large projects; the setting up of a "bad" bank; the securitisation of commercial and industrial loans; the transfer of catastrophe risk to financial markets; agency in insurance; and dealing with a run on an insurance company.
Interest Rate Models
LIBOR market models, HJM models, affine models, pricing and hedging, numerical methods, calibration
Financial Risk Management
In 2010 I completed my Bachelor of Mathematics at the University of Waterloo. I am one of the first graduates of the new Financial Analysis and Risk Management program.
Below you can see a list of brief descriptions of the undergraduate courses that I have taken:
Mathematics of Finance
The theory of rates of interest and discount including the theoretical continuous case of forces of interest and discount. Annuities and sinking funds, including the continuous case. Practical and theoretical applications primarily to mortgages and bonds. Yield rates.
Introduction to Actuarial Mathematics
The economics of insurance, utility theory. Application of probability to problems of life and death. The determination of premiums for insurances and annuities in both the discrete and continuous case.
Corporate Finance 1
Time value of money. Introduction to corporate finance in a mathematical setting. Description and valuation of financial instruments, including stocks, swaps and options. Real options. Investment decisions. Capital budgeting and depreciation.
Corporate Finance 2
Investment decision using Markowitz and utility theory. Capital Asset Pricing Model. Arbitrage Pricing Theory. Market efficiency. Capital structure and dividend policy. Advanced topics.
Mathematical Models in Finance
Mathematical techniques used to price and hedge derivative securities in modern finance. Modelling, analysis and computations for financial derivative products, including exotic options and swaps in all asset classes. Applications of derivatives in practice.
Advanced Corporate Finance
This course will cover various topics in advanced Corporate Finance, including real options, inventory models and management, corporate governance, asymmetric information and signalling, agency theory and corporate incentives.
Introduction to Financial Accounting
This course is an introduction to financial accounting. The preparation and use of financial statements is examined. The accounting cycle, assets and liabilities reporting, is discussed.
Introduction to Managerial Accounting
This course is an introduction to the preparation and use of accounting information for management decision-making and reporting. Cost behaviour, cost accumulation systems and short and long-term decision models are discussed.
This course describes the environment in which individual investors, institutional investors, security analysts, and investment advisors operate. Students will develop knowledge of current techniques used in asset valuation, portfolio management, and financial planning.
Differential Equations for Business and Economics
First order linear and separable differential equations. Exponential growth with applications to continuous compounding. The logistic equation and variations. Introduction to systems of linear differential equations in R2. Dimensional analysis. Linear partial differential equations. Boundary value problems. The diffusion equation. Solutions to the Black-Scholes partial differential equations. Introduction to numerical methods.
Introduction to Business Organization
An introduction to the topic of Canadian business organization and management. Topics include the Canadian business environment, theories of management thought, forms of ownership, corporate structure and growth, the process of management - planning, organization theory, motivation, control and communication.
Functional Areas of the Organization
An introduction to managerial aspects of the specific areas of marketing, production, finance, personnel and industrial relations.
Introduction to Marketing Management
This survey course introduces the student to the basic concepts of marketing. Emphasis is placed on consumer and environmental analysis, marketing strategy and the marketing mix. The course is designed to provide students with a broad understanding of the marketing process from the viewpoint of the marketing manager. The teaching method is lecture and discussion.
Business Policy 1
Business Policy I is the first of two courses dealing with strategic management, and providing an understanding of the process of strategy formulation and implementation. The course is case-oriented and integrates concepts from other more specialized courses.
First-Year Chinese 1
An introductory course for students who have little or no prior background in writing, speaking, or understanding any dialect of the Chinese language to develop basic listening, speaking, reading and writing skills. Practical oral and written exercises are used to provide a firm grammatical foundation for further study.
First-Year Chinese 2
With the completion of the study of the rudiments of phonetics (as provided in CHINA 101R), the emphasis in this course shifts to grammar and character writing. Vocabulary will be expanded to between 500 and 700 words.
Second-Year Chinese 1
Development of speaking, writing, reading, and listening skills. This course and its follow-up (CHINA 202R) include a survey of grammar, complex sentences and logical stress.
A first course in optimization, emphasizing optimization of linear functions subject to linear constraints (linear programming). Problem formulation. Duality theory. The simplex method. Sensitivity analysis.
Portfolio Optimization Models
Applications of basic optimization models and techniques for decision making in financial markets. Quadratic optimization subject to linear equality constraints. Derivation of efficient portfolios and the Markowitz efficient frontier. The Capital Market Line. Practical portfolio optimization as a quadratic programming problem. A solution algorithm for quadratic programming problems.
Intermediate Accounting for Finance
This intermediate level accounting course will focus on the usage of financial information from a management perspective.
Financial Statement Analysis
This advanced course in financial statement analysis provides a framework for using financial statement data in a variety of business analysis and valuation contexts.
Developing Programming Principles
Review of fundamental programming concepts and their application in Java. Arrays of simple types. Objects: encapsulation, instantiation, declaration and use, exceptions. Practical programming: design and life-cycle issues. Arrays of objects. Libraries and interactive programming.
Principles of Computer Science
An introduction to basic concepts of computer science, including the paradigms of theory, abstraction, and design. Broad themes include the design and analysis of algorithms, the management of information, and the programming mechanisms and methodologies required in implementations. Topics discussed include iterative and recursive sorting algorithms; lists, stacks, queues, trees, and their application; and the history and philosophy of computer science.
Management Information Systems
An introduction to information systems and their strategic role in business. Topics include types of information systems, organizational requirements, systems development strategies, decision support systems, data and information management, and information systems management, control and implementation.
Introduction to Microeconomics
This course provides an introduction to microeconomic analysis relevant for understanding the Canadian economy. The behaviour of individual consumers and producers, the determination of market prices for commodities and resources, and the role of government policy in the functioning of the market system are the main topics covered.
Introduction to Macroeconomics
This course provides an introduction to macroeconomic analysis relevant for understanding the Canadian economy as a whole. The determinants of national output, the unemployment rate, the price level (inflation), interest rates, the money supply and the balance of payments, and the role of government fiscal and monetary policy are the main topics covered.
Macroeconomic Theory 1
Theory of the determination of income/output (GDP), employment, unemployment, prices (inflation), and interest rates; an analysis of monetary and fiscal policy.
Communications in Mathematics & Computer Science
This course aims to build students' oral and written communication skills to prepare them for academic and workplace demands. Working independently and in collaboration with others, students will analyze and produce various written and spoken forms of communication. Projects and assignments will draw on materials for Mathematics and Computer Science students.
Algebra for Honours Mathematics
A study of the basic algebraic systems of mathematics: the integers, the integers modulo n, the rational numbers, the real numbers, the complex numbers and polynomials.
Linear Algebra 1 for Honours Mathematics
Systems of linear equations, matrix algebra, elementary matrices, computational issues. Real and complex n-space, vector spaces and subspaces, basis and dimension, rank of a matrix, linear transformations and matrix representations. Inner products, angles and orthogonality, applications.
Calculus 1 for Honours Mathematics
Rational, trigonometric, exponential, and power functions of a real variable; composites and inverses. Absolute values and inequalities. Limits and continuity. Derivatives and the linear approximation. Applications of the derivative, including curve sketching, optimization, related rates, and Newton's method. The Mean Value Theorem and error bounds. Introduction to the Riemann Integral and approximations. Antiderivatives and the Fundamental Theorem. Change of variable, areas and rate integrals. Suitable topics are illustrated using computer software.
Calculus 2 For Honours Mathematics
Review of the Fundamental Theorem. Methods of integration. Further applications of the integral. Improper integrals. Linear and separable differential equations and applications. Vector (parametric) curves in R2. Convergence of sequences and series. Tests for convergence. Functions defined as power series. Taylor polynomials, Taylor's Theorem, and polynomial approximation. Taylor series. Suitable topics are illustrated using computer software.
Linear Algebra 2 for Honours Mathematics
Orthogonal and unitary matrices and transformations. Orthogonal projections, Gram-Schmidt procedure, best approximations, least-squares. Determinants, eigenvalues and diagonalization, orthogonal diagonalization, singular value decomposition, applications.
Calculus 3 for Honours Mathematics
Calculus of functions of several variables. Limits, continuity, differentiability, the chain rule. The gradient vector and the directional derivative. Taylor's formula. Optimization problems. Mappings and the Jacobian. Multiple integrals in various co-ordinate systems.
Introduction to Combinatorics
Introduction to graph theory: colourings, matchings, connectivity, planarity. Introduction to combinatorial analysis: generating series, recurrence relations, binary strings, plane trees.
Introduction to the concepts of learning, person perception, attitudes and motivation in an organization. Consideration of communication, roles, norms and decision making within a group. Discussion of power, control, leadership and management in light of the above concepts.
Commercial and Business Law for Mathematics Students
The Judicial Process, Contract Law, Agency, Bankruptcy, Negotiable Instruments, Law of Banking, Insurance Law, Partnership Law, Company Law, Torts, Real Estate Law.
The laws of probability, discrete and continuous random variables, expectation, central limit theorem.
Empirical problem solving, measurement systems, causal relationships, statistical models, estimation, confidence intervals, tests of significance.
Applied Linear Models
Modeling the relationship between a response variable and several explanatory variables (an output-input system) via regression models. Least squares algorithm for estimation of parameters. Hypothesis testing and prediction. Model diagnostics and improvement. Algorithms for variable selection. Nonlinear regression and other methods.
Review of basic probability. Generating functions. Theory of recurrent events. Markov chains, Markov processes, and their applications.
Statistics for Business 2
Analysis of time series data in business; adjustment and over-adjustment; forecasting using simple models. Process thinking and improvement; design and analysis of process investigations.