AMS 603 Risk Measures for Finance and Data Analysis
Risk analysis is an important to quantitative finance, insurance, commercial credit and many areas of data analysis. We emphasize risk analysis methods that capture observed features of risk, such as heavy tails, and validation of risk models against observed data. Students will be graded on the basis of projects drawn from multiple asset classes considered in the course work, including fixed income, options, portfolio optimization and foreign exchange. Professional standards for software development will be followed. Guest lectures by industry leaders will be included. Participation via conferencing software will be available as an option to class attendance.
3 credits, ABCDF grading
NOTE: There are no prerequisites; intellectual maturity is assumed.
Participation via conferencing software will be available as an option to class attendance.
Textbooks:
Required:
“The Mathematics of Financial Derivatives, A Student Introduction" by Paul Wilmott, Sam Howison and Jeff Dewynne; 1st edition, published by Cambridge University Press, 1995, ISBN: 978-0521497893
Recommended for Supplementary Reading:
"Derivatives: The Theory and Practice of Financial Engineering (Wiley Frontiers in Finance Series)" by Paul Wilmott; published by John Wiley & Sons, Ltd.; 1998; ISBN: 978-0471983897
"Machine Learning: An Applied Mathematics Introduction" by Paul Wilmott; publisehd by Panda Ohana Publishing; 2013, ISBN: 978-1916081604
"Levy Processes and Stochastic Calculus" by David Applebaum; Cambridge University Press, 2nd edition, January 2019, ISBN: 9780511809781
"Credit Risk Modeling: Theory and Applications" by David Lando; Princeton University Press, 2004; ISBN: 9780691089294
"Levy Processes in Credit Risk: by Wim Schoutens and Jessica Caribani; John Wiley & Sons, 2010, ISBN: 9780470685068
Course Objectives/Learning Outcomes:
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- AMS 603 is designed as a terminal course, to transition from traditional lecture based
learning to a world where learning (which should always continue) is basically self
directed.
- AMS 603 is designed as a terminal course, to transition from traditional lecture based
learning to a world where learning (which should always continue) is basically self
directed.
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- Risk models start with a common sense and intuition understanding of the risk. Not
all risks can or should be modeled analytically; for some risks the intuitive understanding
is the end of the story.
- Analytic risk models, for important risks, are first developed using simple tools.
These are then refined to give professional quality risk models.
- Mathematically, risk models are built by a combination of two simple ideas. The first
is clustering, as bad events are not uniformly distributed, but occur in clusters.
The second idea is known as heavy tails. Bad events happen more frequently that simple
models of a random process would suggest. The analytical risk models depend on market
data. Data sufficient for this course is available from the www.
- The analytic models that process the data require programming skills. Generally speaking,
python is sufficient as a programming model. A review lecture on the use of python
in typical risk model algorithms is included. Machine learning based alpha strategies
will be developed. The use of linear programming for the optimization of large portfolios
is explained.
- Risk models are developed for the major asset classes: equities, foreign exchange,
commodities, options, and fixed income (the term structure of interest). Specialized
analytical models to capture unique dominant features these asset classes are included.
- The midterm exam is to develop and evaluate a risk model. The final exam is to present a professional lecture, suitable as an employment lecture, developing ideas presented in the course.