## Courses

**AMS 511, Foundation of Quantitative Finance **

Introduction to capital markets, securities pricing, and modern portfolio theory,
including the organization and operation of securities market, the Efficient Market
Hypothesis and its implications, the Capital Asset Pricing Model, the Arbitrage Pricing
Theory, and more general factor models. Common stocks and their valuation, statistical
analysis, and portfolio selection in a single-period, mean-variance context will be
explored along with its solution as a quadratic program. Fixed income securities and
their valuation, statistical analysis, and portfolio selection. Discussion of the
development and use of financial derivatives. Introduction to risk neutral pricing,
stochastic calculus, and the Black-Scholes Formula. Whenever practical, examples will
use real market data. Numerical exercises and projects in a high-level programming
environment will also be assigned.

*Prerequisites:
AMS 510
*

3 credits, ABCF grading

AMS 511 webpage

**AMS 512 Capital Markets and Portfolio Theory **

Development of capital markets and portfolio theory in both continuous time and multi-period
settings. Utility theory and its application to the determination of optimal consumption
and investment policies. Asymptotic growth under conditions of uncertainty. Applications
to problems in strategic asset allocation over finite horizons and to problems in
public finance. Whenever practical, examples will use real market data. Numerical
exercises and projects in a high-level programming environment will also be assigned.

*Prerequisite:
AMS 511
*

3 credits, ABCF grading

AMS 512 webpage

**AMS 513 Financial Derivatives and Stochastic Calculus **

Further development of derivative pricing theory including the use of equivalent martingale
measures, the Girsanov Theorem, the Radon-Nikodym Derivative, and a deeper, more general
understanding of the Arbitrage Theorem. Numerical approaches to solving stochastic
PDEÕs will be further developed. Applications involving interest rate sensitive securities
and more complex options will be introduced. Whenever practical, examples will use
real market data. Numerical exercises and projects in a high-level programming environment
will also be assigned.

*Prerequisite:
AMS 511
*

3 credits, ABCF grading

AMS 513 webpage

**AMS 514 Computational Finance **

Review of foundations: stochastic calculus, martingales, pricing, and arbitrage. Basic
principles of Monte Carlo and the efficiency and effectiveness of simulation estimators.
Generation of pseudo- and quasi-random numbers with sampling methods and distributions.
Variance reduction techniques such as control variates, antithetic variates, stratified
and Latin hypercube sampling, and importance sampling. Discretization methods including
first and second order methods, trees, jumps, and barrier crossings. Applications
in pricing American options, interest rate sensitive derivatives, mortgage-backed
securities and risk management. Whenever practical, examples will use real market
data. Extensive numerical exercises and projects in a general programming environment
will also be assigned.

*Prerequisite:
AMS 512 and
AMS 513
*

3 credits, ABCF grading

AMS 514 webpage

**AMS 515 Case Studies in Computational Finance II **

Actual applications of Quantitative Finance to problems of risk assessment, product
design, portfolio management, and securities pricing will be covered. Particular attention
will be paid to data collection and analysis, the design and implementation of software,
and, most importantly, to differences that occur between Òtheory and practiceÓ in
model application, and to the development of practical strategies for handling cases
in which Òmodel failureÓ makes the naive use of quantitative techniques dangerous.
Extensive use of guest lecturers drawn from the industry will be made.

*Prerequisite:
AMS 512 and
AMS 513
*

3 credits, ABCF grading

AMS 515 webpage

**AMS 516, Statistical Methods in Finance**

The course introduces statistical methodologies in quantitative finance. Financial
applications and statistical methodologies are intertwined in all lectures. The course
will cover regression analysis and applications to the Capital Asset Pricing Model
and multifactor pricing models, principal components and multivariate analysis, statistical
methods for financial time series; value at risk, smoothing techniques and estimation
of yield curves, and estimation and modeling of volatilities.

3 credits, ABCF grading

AMS 516 webpage

**AMS 517, Risk Management **

Quantitative methods for risk management problems including market risk, credit risk,
operational risk and Basel II accord. Multivariate models; extreme value theory; structure
and reduced-form models of default; and copula-based models.

*Prerequisite:
AMS 511,
AMS 512, and
AMS 513
*

3 credits, ABCF grading

AMS 517 webpage

**AMS 518, Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization**

The course provides a thorough treatment of advance risk measurement and portfolio
optimization, extending the traditional approaches to these topics by combining distributional
models with risk or performance measures into one framework. It focuses on, among
others, the fundamentals of probability metrics and optimization, new approaches to
portfolio optimization and a varierty of essential risk measures. Numerical exercises
and projects in a high-level programming environment will be assigned.

*Prerequisite:
AMS 512 or instructor consent
*

Offered Fall semester

3 credits, ABCF grading

AMS 518 webpage

**AMS 519, Internship in Quantitative Finance**

Supervised internship in financial institution. Students will typically work at a
trading desk, in an asset management group, or in a risk management group. Students
will be supervised by a faculty member and a manager at their internship site. Written
and oral reports will be made to both supervisors.

Offered every semester

3-6 credits, S/U Grading

AMS 519 webpage

**AMS 522, Bayesian Methods in Finance**

The course explores in depth the fundamentals of the Bayesian methodology and the
use of the Bayesian theory in portfolio and risk management. It focuses on, among
other topics incorporating the prior views of analysts and investors into the asset
allocation process, estimating and predicting volatility, improving risk forecasts,
and combining the conclusions of different models. Numerical exercises and projects
in a high-level programming environment will be assigned.

*Prerequisite:
AMS 512 or instructor consent
*

Offered Spring semester

3 credits, ABCF grading

AMS 522 webpage

**AMS 523, Mathematics of High Frequency Finance**

The course explores Elements of real and complex linear spaces. Fourier series and
transforms, the Laplace transform and z-transform. Elements of complex analysis including
Cauchy theory, residue calculus, conformal mapping and Möbius transformations. Introduction
to convex sets and analysis in finite dimensions, the Legendre transform and duality.
Examples are given in terms of applications to high frequency finance.

Offered Fall semester

3 credits, ABCF grading

AMS 523 webpage

**AMS 600, Socially Responsible Investing**

Introduction to a scope of investments which are socially responsible because of the
nature of the business the company conducts, including but not limited to: avoiding
investment in companies that produce or sell addictive substances (like alcohol, gambling
and tobacco) and seeking out companies engaged in environmental sustainability.

*Prerequisite:
AMS 511
*

Course is cross-listed with MBA 581

Offered Fall semester

3 credits, ABCF grading

AMS 600 webpage

**AMS 601, Risk Management and Business Risk Control in BRIC Countries**Introduction to the challenges and opportunities in investing in the BRIC countries,
Brazil, Russia, India and China, with emphasis in the risk assessment, control and
management. Opportunities in investing in BRIC: growth in infrastructure, middle
class demand, educated cheap workforce, potential for outsourcing work, high risk/high
reward.

*Prerequisite: AMS 511*

Course is cross-listed with MBA 584

Offered Spring semester

3 credits, ABCF grading

AMS 601 webpage