Teaching

I have taught the following classes over the years

IEOR E4731: Credit Risk Modeling and Credit Derivatives

Credit risk is a topic of fundamental importance in modern banking systems. Quantitative credit risk methodologies play a fundamental role in the risk-management divisions of major investment banks. The recent crisis has led to numerous regulatory reforms requiring banks to comply with capital requirements. This can only be achieved via the implementation of a sophisticated and mathematically sound credit risk framework. This course deals with quantitative modeling and measuring of credit risk. You will learn how to price financial instruments, whose payoff is contingent to the realization of a credit event. Those instruments include corporate bonds, and credit default swaps. You will also learn how to measure credit losses, and calibrate financial models to using market data. Topics of high recent interest in the financial industry and the regulatory space, including counterparty risk, systemic risk, derivative clearinghouses, and valuation adjustments will be discussed.

IEOR E4709: Statistical Analysis and Time Series

Statistics and Time series Analysis plays a fundamental role in the construction, testing, and validation of models used in the financial industry, and otherwise. The class covers the foundational tools of statistics and time series analysis, with strong focus on their applications to financial data. The course emphasizes empirical analysis of asset prices, such as heavy tails and predictability tests for stock returns. It discusses simple and multiple linear regressions along with their applications to the mortgage market and market making. We also discuss Hypothesis Testing, maximum Likelihood Estimation, Bayesian Statistics, time series analysis, ARCH and GARCH models. The course develops applications of time series to transactions costs analysis, market microstructure, and energy markets.

IEOR 8100: Networks: Games, Contagion, and Control

Networks are ubiquitous in our modern society. Economic and social networks have been used extensively to model a variety of situations, in which individual decision-makers are affected by the choices of their peers in the network. For instance, the choices of individuals regarding which products to buy or whom to vote for are usually influenced by their friends and colleagues. The decision of an individual or a firm on whether or not to adopt a new technology (new software, messaging service, etc.) depends on who among their social or professional network are adopting that technology as well. Banks in financial networks may coordinate private or subsidized bailouts and rescue insolvent banks so as to stop financial contagion. The decision of an individual to become a criminal depends heavily on the behavior of others in his/her social network: more connections to criminals yield a higher profitability in the crime business and thus a higher chance of engaging in criminal activities. This course will introduce the main mathematical models for the study of these networks. It will discuss game theoretical and dynamic optimization techniques, which can be used to analyze a wide variety of these networks, including their resilience to shocks, the amplification effects resulting from their topological structure, and how the strategic behavior of network agents shapes the performance of the network.

IEOR E4707: Continuous Time Asset Pricing

Continuous Time Asset Pricing lies at the heart of the modern theory of financial engineering . In this course, we distinguish between complete markets, in which there is a unique no-arbitrage price, and incomplete markets, where absence of arbitrage is not sufficient to obtain uniqueness of prices. We focus mostly on the framework of Brownian Motion driven models. The benchmark model will be the Black-Scholes-Merton pricing model, but we will also cover more general models, such as local and stochastic volatility models. We will discuss both the Partial Differential Equations approach, and the Martingale approach. They are related through the notion of the Feynman-Kac theorem. We also discuss optimal portfolio investment in the above mentioned models, and discuss relationship to pricing and risk management.

IEOR E4602: Quantitative Risk Management

Risk Management is a topic of fundamental importance in financial markets. Quantitative risk management frameworks must be able to identify, quantify, and mitigate risks. There are various sources of risk faced by market participants, including market, credit, liquidity, and operational risk. The global 2007-2009 financial crisis has led to numerous regulatory reforms, which required banks to comply with more stringent capital requirements, including value at risk, expected shortfall, and maximum shortfalls. It also led to the introduction of financial utilities, such as clearinghouses, which collect all risk in the system and insulate each party against the default of the other. This course deals with quantitative modeling and measuring of risk. You will learn how to design risk management procedure which accounts for correlated risk sources, and how to simulate systems to evaluate the resulting risk. We introduce financial instruments that are used to mitigate risk, such as credit default swaps. Time allowing, we also discuss topics of recent interest in the financial industry and the regulatory environment, including systemic risk measures, liquidity coverage ratio requirements to deal with liquidity risk, and procedures to assess funding risk.