Research I work in various areas within the fields of Financial
Statistics, Financial Engineering and Applied Probability. These areas
include
Option Pricing, Optimal Trading Strategies, Stochastic Optimal Control,
and Stochastic Processes. The method I developed for
pricing Asian Options is widely used both in academia and the finance
industry as a benchmark. My
research interests also include
Statistics in Sports.
Pospisil, L., J. Vecer
(2008): "Portfolio Sensitivities to the Changes in the Maximum and the
Maximum Drawdown" (.pdf).
Pospisil, L., J. Vecer, M. Xu (2008): "Tradeable Measures of
Risk" (.pdf).
Pospisil, L., J. Vecer, O. Hadjiliadis (2008): "Formulas for
Stopped Diffusion
Processes with Stopping Times based on Drawdowns and Drawups" (.pdf)
Vecer, J., F. Kopriva, T.
Ichiba (2008):
"Estimating the Effect of the Red Card in Soccer - When to Commit an
Offense in Exchange for Preventing a Goal Opportunity" (.pdf)
Published(ordered by research area):
Mathematical Finance:
Pospisil, L., J. Vecer: (2008): "PDE
Methods for the Maximum Drawdown", Journal of Computational Finance,
forthcoming (.pdf).
Vecer, J. (2007): "Preventing Portfolio Losses by Hedging Maximum
Drawdown", Wilmott, Vol. 5, No. 4 (.pdf,
.ps).
Chiara, N., M. Garvin, J. Vecer (2007): "Valuing Simple
Multiple-Exercise Real Options in Infractructure Projects",
Journal of
Infrastructure Systems, Vol. 13, No. 2, 97-104 (.pdf).
Vecer, J. (2006): "Maximum Drawdown and Directional Trading",
Risk, Vol. 19, No. 12, 88-92 (.pdf,
.ps).
Reprinted in Asia Risk, February 2007, 38-42.
Jonsson, M., J. Vecer (2005): "Insider Trading in Convergent
Markets",Applied Mathematical Finance, Vol. 12, No. 3, 243-252
(.pdf.,
.ps).
Vecer, J., M. Xu (2004): "Pricing Asian
Options in a Semimartingale Model", Quantitative Finance, Vol. 4, No.
2, 170-175 (.pdf, .ps).
Vecer, J. (2002): "Unified Asian Pricing",Risk, Vol. 15, No. 6, 113-116 (.pdf,
.ps).
Implementation in MATLAB: asiancontinuous.m,
Implemenation in Mathematica: AsianOption.nb
Vecer, J. (2001): "A new PDE approach for
pricing arithmetic average Asian options", Journal of Computational
Finance,
Vol. 4, No. 4, 105-113 (.pdf, .ps).
Vecer, J., S. Shreve (2000): "Upgrading
your passport", Risk, Vol. 13, No. 7, 81-83 (.ps).
Shreve, S., J. Vecer (2000): "Options on
a Traded Account: Vacation Calls, Vacation Puts and Passport Options",
Finance and Stochastics, Vol. 4, No. 3, 255-274, (Springer
Verlag) (.ps).
Applied Probability:
Hadjiliadis, O., J. Vecer (2006): "Drawdowns Preceding Rallies
in Brownian Motion Model",Quantitative Finance, Vol. 6, No. 5,
403-409 (.pdf,
.ps).
Vecer, J., M. Xu (2004): "Mean Comparison Theorem cannot be
extended to Poisson case", Journal of Applied Probability, Vol. 41, No.
4, 1199-1202 (.pdf,
.ps).
Quantitative Analysis in Sports:
Vecer, J., T. Ichiba, M.
Laudanovic (2007): "On Probabilistic Excitement of Sports Games",
Journal of Quantitative Analysis in Sports, Vol. 3, No. 3, Article 6 (.pdf, .ps).
Vecer, J. (2004): "Optimal Control for Squash Player", Journal of
Chinese Statistical Association, Vol. 42, No. 2, 92-99 (.pdf, .ps).
Teaching
Present Courses
(Fall 2008):
G8273: Topics in Mathematical Finance
Past Courses:
W4105: Probability (Spring 2006)
W4150: Introduction to
Probability and Statistics (Falls 2002-03)
W4606: Elementary Stochastic Processes (Springs 2003-04)
W6501: Stochastic Processes and Applications I (Falls 2001-02, Falls
2004-06, Spring 2008)
G6505: Stochastic Methods in Finance (Springs 2002-05, 08, Falls
2005-06)
G7010: Topics in Risk (Spring & Fall 2006, coorganizer)
W7040: Statistics in Sports (Spring 2006, 08)
G8273: Topics in Mathematical Finance (Spring 2005)
G8275: Management of Extreme Financial Events (Fall 2006)
G9003/G9004: Seminar in Advanced Probability (Falls 2001&2003,
Springs 2002&2004)
Graduate Students
PhD:
Petr Novotny (2009 - expected): Optimal Portfolio Execution and
High
Frequency Financial
Data.
Libor Pospisil (2008): Risk Measures and Maximum
Drawdown.
Nicola
Chiara (2006): Real Option Methods for Improving Economic
Risk Management in Infrastracture Project Finance (Department of Civil
Engineering, co-sponsor with Prof Michael Garvin)
Olympia
Hadjiliadis
(2004): Change-point Detection of Two-sided Alternatives in the
Brownian Motion Model and its Connection to the Gambler's Ruin Problem
with Relative Wealth Perception.
MSc:
Daisuke
Nakajima (2004): Point
Detection for Poisson Disorder - Application in
Earthquake Occurence in Northern California, 1910 - 1999.
Wei Zhu (2003): Stock Volatility
and Option
Pricing.
Grant Support
NSF Award, DMS 0418457, Decision Analysis in the Presence of Jump
Risk,
09/01/2004 - 08/31/2007 (Jan Vecer, PI)
NSF Award, EAR 0229846, A Stochastic Differential Equation
Approach to
Studying Landslide Failure and Size Distributions, 05/15/2003 -
04/30/2006 (Colin Stark, PI, Jan Vecer, Co-PI)
Miscellaneous
Inventor ofTennis
Analyser,featured technology of Columbia University Here is
a
related article about it in the 09/18/2006 issue of the Business Week
Recently, I have
proposed to study Maximum
Drawdown(the
largest drop in the market) in the relationship with portfolio
insurance: Here is
a report that appeared on 12/18/2006 on the N-TWO
Capital Market website Here
it got mentioned in the 01/22/2007 issue of the Derivatives Week Here
is an article from the 06/18/2007 issue of Barron's