The School of Mathematics at the University of Minnesota is holding a 10-day workshop on Mathematical Modeling in Industry. The workshop is designed to provide graduate students with first hand experience in financial mathematics research.
Students will work in teams of up to 6 students under the guidance of a mentor from the financial modeling/trading sector. The mentor will help guide the students in the modeling process, analysis and computational work associated with a real-world financial modeling/trading problem. A progress report from each team will be scheduled during the period. In addition, each team will be expected to make an oral final presentation and submit a written report at the end of the 10-day period.
There will be 4 teams participating in the workshop.
| Team | Mentor(s) | Affiliation | Topic / Presentation |
|---|---|---|---|
| 1 | Christopher Bemis | Whitebox Advisors | A Study of Equivalence in CVaR Portfolio Optimization |
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A commonly used risk metric in modern finance is Conditional Value at Risk, or CVaR. In contrast to the seminal Mean-Variance optimization, the CVaR setting allows for more flexibility in that there is no a priori assumption regarding the joint distribution of asset returns. Even so, there are many similarities between the two risk metrics. For example, if the underlying returns are assumed jointly normal, there is an equivalence between Mean-Variance optimal portfolios and CVaR optimal portfolios. In the present work, we will examine the impact of linear constraints on a CVaR optimal portfolio and produce results relating to the underlying distribution of returns used in the optimization. In the Mean-Variance setting, one may show that linear constraints may be dropped by perturbing the covariance matrix of the underlying assets. The CVaR setting is necessarily more general, and we seek to obtain results that interpret the impact of linear constraints on the joint distribution of returns in a meaningful way. | |||
| 2 | Christopher Prouty | Cargill | Financial Information Exchange (FIX) |
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Over the past decade, the rise of automated or algorithmic trading has been astounding. An increasing number of firms now employ sophisticated hardware and highly optimized software to place trades and make markets in a variety of asset classes. The volume of trades on electronic exchanges has grown along with the number of firms utilizing automated trading. By some estimates, high frequency trading now accounts for 75% of all trades in US equities. One of the tools employed in automated trading is a protocol called FIX, or Financial Information eXchange. FIX is an open protocol used by banks, hedge funds, exchanges, and other market participants to transmit order and quote data between trading partners. Although FIX as a protocol is fairly simple, implementation requires solid knowledge in both programming and finance. Participants in the FIX module will build a functioning FIX client in C# and use it to connect to a proprietary server application generating artificial market data. Using FIX, participants will capture a stream of quotes from the server and then analyze the time series to try to design a profitable trading strategy. Once a strategy is designed and implemented in the client application, trades will be placed with the server via FIX, and P&L of the strategy will be tracked. Ideally, the team will complete the module by building a fully automated profitable trading strategy. | |||
| 3 | Jason Vinar | Ameriprise | The SABR Volatility Model |
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The Black-76 model has been the standard model for European options on currency, interest rates, and stock indices with it's main drawback being the constant volatility assumption. The SABR (stochastic, alpha, beta, and rho) model is a stochastic model which attempts to capture the volatility smile. The model has many attractive features including the ability to analytically derive the Black volatility given the forward and strike price, transform to local volatility for Monte Carlo simulation, and the parameters relate to observable market volatilities. We will explore the models' behavior through Monte Carlo simulation by pricing a vanilla option and a path-dependent barrier option. As Monte Carlo methods are deployed attention will be given to increase the efficiency of the simulation algorithm and reduce the variance of the estimates. We will look to improve simulation results through the discretization of the stochastic differential equations, random number generation, and antithetic variates. As a final step, with time permitting, participants will calibrate the SABR model to actual market volatilities and develop a scheme to dynamically hedge the barrier option with vanilla options, interest rate swaps, and futures. | |||
| 4 | Lourenco Miranda and Swati Agiwal | US Bank Corporate | Treasury Quantitative Risk Management |
| Option to Default: Counterparty Credit Risk in OTC Derivatives | |||
Events are in STSS 131A unless noted.
Team break-out rooms are the same for all workshop days: Team 1 - STSS 131A, Team 2 - STSS 119, Team 3 - STSS 121, Team 4 - STSS 117.
All Day Workshop Outline: Posing of problems by the 4 industry mentors.
Half-hour introductory talks in the morning followed by a welcoming lunch.
In the afternoon, the teams work with the mentors.
The goal at the end of the day is to get the students to start working on the projects.
Friday, January 6 to Sunday, January 8All Day Students work on the projects. Mentors guide their groups through the modeling process, leading discussion sessions, suggesting references, and assigning work.
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Monday, January 9
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Tuesday, January 10 to Friday, January 13All Day Students work on the projects in their breakout rooms. Mentors available for consultation.
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Keller Hall, Room Second Floor - Room 2-260 for the days events.
Dr. Swati Agiwal is a quantitative analyst in the Corporate Treasury Department at US Bank in Minneapolis. Among other facets of her job at the Bank, Ms. Agiwal is responsible for developing and enhancing Internal Capital Adequacy Assessment Processes (ICAAP)/Economic Capital framework and quantitative models for Business Risk, Credit Risk in investment securities, Market Risk for compliance with Market Risk Rule, Operational Risk models for compliance with Advanced Measurement Approach under Basel I and Basel II/ICAAP The author of various papers in economics journals and presentations at conferences, Dr. Agiwal holds a Ph.D. in Applied Economics with a Minor in Business Administration (Finance), and an M. S. in Applied Economics from the University of Minnesota. She also holds an M. A. in Economics and a B. S. in Statistics from the University of Mumbai.
Dr. Chris Bemis is a quantitative analyst for Whitebox Advisors, working primarily on equity market modeling outside of the United States. He is also an active researcher for the Whitebox quantitative group, where he works on varied problems in the context of equity, derivative, and fixed income strategies. Dr. Bemis earned his PhD in applied mathematics from the University of Minnesota. His thesis work involved both modeling and optimization for portfolios of risky assets.
Dr. Lourenco Miranda is Vice President (Quantitative Development) at U.S. Bank in Minneapolis, MN. In that capacity, Dr. Miranda is responsible for quantitative modeling within Corporate Treasury. Before that, he was Senior Risk Officer for the International Finance Corporation (IFC), the private sector arm of the World Bank Group. There, Lourenco worked as a global advisor to IFC financial markets Clients in developing or frontier countries, assisting local Banks to implement or improve their internal risk management practices. Lourenco has hands-on experience in banking and finance in more than 30 countries in South America, South and East Asia and Eastern Europe. Before the World Bank, Lourenco held other positions in financial institutions like ABN AMRO Bank and Santander Investment Bank, with more than 14 years of relevant experience in the industry. In the academic arena, Lourenco has worked in different academic centers in the world, such as in Brazil, the Netherlands and Russia, working as a visiting professor or research collaborator. For a long period of time, Lourenco was also the Regional Director for the Global Association of Risk Professionals (GARP) in Brazil. He holds a PhD in Statistical Physics and - apart from all that - Lourenco is father of triplets.
Christopher Prouty serves as the instructor for FM 5091/5092: Programming and Presentation in Finance and works for Cargill. Chris began his financial career as a research assistant at the Federal Reserve Bank in Minneapolis. Since graduating from the University of Minnesota with a B.S. in Applied Economics, Chris has worked in commodities and insurance, in roles focusing on trading and risk management through derivative strategies. Chris currently works for Cargill, where he is an exotic derivatives trader. During college and shortly thereafter Chris operated a small software consulting firm, CP Consulting. He has completed freelance software development projects for Twin Cities firms, including the University of Minnesota Foundation and ACR ATI, a firm which offers employee testing services to the health care industry.
Jason Vinar is a Financial Engineer at Ameriprise Financial in the Quantitative Strategies Group. He works in a team involved in the design, development and implementation of financial applications and hedging platforms for the variable annuity living benefit riders within Ameriprise Financial. He is also involved in mathematical modeling and programming, platform architecture and data management for the living benefit rider product. Previously Mr. Vinar was a Partner at Castle Peak Capital Advisors where he was responsible for model development and implementation for residential mortgage related products. He was also an Analytics Manager for the PIA unit at GMAC-ResCap. In this capacity he was responsible for managing the trading analytics and risk management functions of the PIA. Prior to that, he was Project Lead/Lead Developer for Financial Engineering projects in the Risk and Value Analytics group of GMAC-ResCap. Jason holds a Master's degree in Financial Mathematics from the University of Minnesota and Bachelor's degrees, in Mathematics and Economics, from the University of Wisconsin, Eau Claire.
Winter 2011 workshop website
Winter 2010 workhop website