Financial Mathematics Modeling for Graduate Students
Winter 2013 Workshop: January 10-19, 2013)
The School of Mathematics at the University of Minnesota holds a 10-day
workshop on Financial Mathematics Modeling every winter between Fall and
Spring Semesters. Below are the details for the Winter 2013 Modeling
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.
Projects and Industry Mentors
There will be 4 teams participating in the workshop.
Topic / Presentation
Christopher Prouty, Exotics Trader and Instructor
Cargill and University of Minnesota MFM Program
Financial Information Exchange (FIX)
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.
Nelson Neale, Market Strategist - Corporate Risk Management
Cash Flow at Risk for Non-Financial Corporations
Value-at-risk (VaR) represents the standard risk measurement and modeling framework for banks, trading firms and other financial corporations. While the metric is particularly useful for those entities holding highly liquid assets like equities, the unique properties and operations of non-financial corporations demand a risk framework that focuses on cash flow or earnings uncertainty over a time horizon that matches the view of management and shareholders. Cash flow-at-risk (CFaR) or earnings-at-risk (EaR) represent extensions of VaR that may be used to effectively evaluate both price and non-price risks associated with these firms.
Participants in this module will develop a functional Monte Carlo simulation-based CFaR framework for a hypothetical agricultural commodity-based corporation. The team will evaluate a variety of spot price processes to describe each cost or revenue component (e.g., geometric Brownian motion, mean reversion, etc.), parameterize models, and identify key risk drivers for the corporation. Based on the identified risk profile, the team will consider risk management options under different management objective scenarios
Zhen Liu, MCFAM Assistant Professor and MFM Instruction
University of Minnesota
Monte Carlo Simulation For Multi - Asset Options and Stochastic Volatility and Jumps Models
Monte Carlo (MC) simulation has become a powerful tool in the pricing of derivative securities and in risk management thanks to its flexibility and power to overcome the difficulty of the course of dimensionality for multi-asset option pricing. In the project, we will study MC methods for multi-asset option pricing and option pricing under stochastic volatility and jumps (SVJ).
In particular we will explore MC methods in two kinds of problems: First, pricing of multi-asset exotic options, including basket options and spread options, with applications in crack options on oil products. We will compare the simulation results with those obtained from approximation formulas and PDE methods, and examine how correlations among different underlying asset prices affect the option prices. Second, we will look at implied volatility surfaces arising in models with stochastic volatility and jumps. Under the SVJ model, we price a series of European put options by simulation and calculate Black-Scholes implied volatility and finally produce a 3D plot of the implied volatility surface.
Throughout the project, students will have chances to implement methods to generate multivariate normal random variables, Poisson random variable, and variance reduction techniques.
Chris Bemis, Portfolio Manager
Statistics and Optimization for High Frequency Data
In this module, we will examine traditional optimization techniques, time series methods, and stylized features such as momentum and reversion for tick data across a variety of equities. Of particular interest will be questions of volatility scaling and detection of statistically significant autoregressive parameters under mild assumptions. The module will provide an introduction for many of the techniques used. Matlab will be encouraged, but the work may be completed within the language that the module feels most comfortable. Tick data will be provided historically in an easily readable format.
Team break-out rooms are the same for all workshop days (*except Friday, January 18, 2013):
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.
9:00am-9:30am Coffee and Registration
9:30am-9:40am Welcome Rina Ashkenazi (University of Minnesota)
9:40am-10:00am Team 1: Financial Information Exchange (FIX) -
Christopher Prouty (Cargill)
10:00am-10:20am Team 2: Cash flow at Risk for Non-Financial Corporations -
Nelson Neale (Land O'Lakes)
10:20am-10:40am Team 3: Monte Carlo Simulation For Multi - Asset Options and Stochastic Volatility and Jumps Models -
Zhen Liu (University of Minnesota)
10:40am-11:00am Team 4: Topic Pending -
Chris Bemis (WhiteBox Advisors & University of Minnesota)
1:30pm-4:30pm Afternoon - start work on projects
Friday, January 11 to Saturday, January 12
All Day Students work on the projects. Mentors guide their groups
through the modeling process, leading discussion sessions, suggesting
references, and assigning work.
2:00pm-5:00pm Remainder of the day students work on projects in breakout rooms. Mentors available for consultation.
Tuesday, January 15 to Friday, January 18
All Day Students work on the projects in their breakout rooms. Mentors available for consultation.
Saturday, January 19
Keller Hall, Room Second Floor - Room 3-210 for the days events.
9:30am Team 1 Final Report
10:00am Team 2 Final Report
10:30am Team 3 Final Report
11:00am Team 4 Final Report
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. Nelson Neale is Market Strategist for Land O'Lakes, a $13 billion food and agricultural cooperative in Arden Hills, MN with over $4 billion in commodity spend. He is responsible for developing programs to identify commodity risk and volatility across the Land O'Lakes portfolio of businesses (cost, revenues, margin management) and to identify and implement solutions to mitigate these risks.
Prior to Land O'Lakes, Nelson served as a member of the Global Risk and Trading practice of Oliver Wyman in New York where he directed North American and European engagements focused on trading, hedging and risk management strategies and programs for oil and gas companies. Nelson has also previously served as head of the market and commodity analysis group for Tyson Foods and as a market risk officer for UBS Investment Bank. He began his career in the quantitative research group at Enron in Houston.
Nelson holds a PhD in engineering from Rice University and a BS in mathematics from Davidson College.
Dr. Zhen Liu is an Assistant Professor within MCFAM (the Minnesota Center for Financial and Actuarial Mathematics) at the School of Mathematics - University of Minnesota. Prior to that he was an Assistant Professor of Engineering Management and Systems Engineering at Missouri University of Science & Technology (formerly University of Missouri-Rolla) and served as the director of Laboratory for Investment & Financial Engineering (LIFE) from 2007 to 2012. He was visiting the Department of Industrial Engineering at Tsinghua University as a senior visiting scholar from July to December in 2009, and was a Givens Research Associate in Mathematics and Computer Science Division at Argonne National Laboratory in 2003. He received his Ph.D. in Industrial Engineering & Management Sciences from Northwestern University in 2007.
His primary research interests are dynamic decision-making under uncertainties with applications in financial engineering/computational finance, energy and healthcare problems and interface between operations & finance.
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.