José Enrique Figueroa-López Assistant Professor of Statistics and Mathematics (courtesy) Purdue University West Lafayette, IN 47907 Office: Math 542. Phone: (765) 494 6036 E-mail: figueroa@stat.purdue.edu

Research interests:

• Mathematical finance: Estimation methods for high-frequency data. High-frequency trading and asset price formation. Portfolio optimization problems in continuous-time models. Emphasis on Lévy-driven and jump-diffusion models.
• Probability and Stochastic processes: Stochastic control, stochastic analysis, and simulation.
• Statistics: Nonparametric estimation methods using sieves, model selection, and adaptive methods.
• Information and coding theory: Concentration inequalities applied to data compression.

Teaching:

• Spring 2012: STAT 473. Actuarial Models II. (Also taught in Spring 2011).
• Previous courses:
• MATH 516/STAT 541. Advanced Probability and Options, with numerical methods. Fall 2011. (Also taught in Fall 2010).
• STAT 598F. Modeling with Jump Processes and Applications to Mathematical Finance. Spring 2010.
• STAT 511. Statistical Methods. Spring 2010.
• MATH 515/STAT 540. Mathematics of Finance. Spring 2009. (Also taught in Spring 2008).

Grants/Awards:

• NSF CAREER Award: Bridging High-Frequency Data Analysis and Continuous-time Features of Lévy Models
  DMS-1149692, 2012-2017. Estimated Total Award Amount: $400,000.
• NSF grant: Nonparametric Methods for Jump Processes Under Microstructure Noise
  DMS-0906919, 2009-2012. Total Award Amount: $107,250.

Research:

• Publications:


• Pricing and semimartingale representations of vulnerable contingent claims in regime-switching markets (with A. Capponi and J. Nisen). To appear in Mathematical Finance.


• Dynamic portfolio optimization with a defaultable security and regime switching (with A. Capponi). To appear in Mathematical Finance.


• Statistical estimation of Lévy-type stochastic volatility models. Annals of Finance 8(2), 309-335, 2012. DOI:10.1007/s10436-010-0150-x.


• Small-time expansions of the distributions, densities, and option prices of stochastic volatility models with Lévy jumps (with R. Gong and C. Houdré). Stochastic Processes and their Applications 122, 1808-1839, 2012. DOI: 10.1016/j.spa.2012.01.013


• Jump-diffusion models driven by Lévy processes. In the Handbook of Computational Finance, J. Duan, J.E. Gentle, and W. Hardle (eds.). Springer, 2012. ISBN: 978-3-642-17253-3.


• The small-maturity smile for exponential Lévy models (with Martin Forde). SIAM Journal on Financial Mathematics 3(1), 33-65, 2012. DOI: 10.1137/110820658.


• Estimation of NIG and VG models for high frequency financial data (with S.R. Lancette, K. Lee, and Y. Mi). In the Handbook of Modeling High-Frequency Data in Finance, F. Viens, M.C. Mariani, and I. Florescu (eds.). J. Wiley, 2011. ISBN: 978-0-470-87688-6.


• Central limit theorems for the nonparametric estimation of time-changed Lévy models. Scandinavian Journal of Statistics 38, 748-765, 2011. DOI:10.1111/j.1467-9469.2010.00728.x.


• Sieve-based confidence intervals and bands for Lévy densities. Bernoulli 17(2), 643-670, 2011. DOI:10.3150/10-BEJ286.


• Approximations for the distributions of bounded variation Lévy processes. Statistics and Probability Letters 80, 1744-1757, 2010. DOI:10.1016/j.spl.2010.07.019.


• State-dependent utility maximization in Lévy markets (with J. Ma). International Journal of Stochastic Analysis, 2010. DOI:10.1155/2010/236587.


• Nonparametric estimation of time-changed Lévy models under high-frequency data . Advances in Applied Probability 41(4), 1161-1188, 2009. DOI:10.1239/aap/1261669591.


• Small-time expansions for the transition distribution of Lévy processes (with C. Houdré). Stochastic Processes and their Applications 119, 3862-3889, 2009. DOI: 10.1016/j.spa.2009.09.002


• Nonparametric estimation for Lévy models based on discrete-sampling. In IMS Lecture Notes-Monograph Series (LNMS). Optimality: The Third Erich L. Lehmann Symposium (editors: J. Rojo). Volume 57, 117-146, 2009. DOI:10.1214/09-LNMS5709.


• Small-time moment asymptotics for Lévy processes. Statistics and Probability Letters 78, 3355-3365, 2008. DOI:10.1016/j.spl.2008.07.012.


• Risk bounds for the non-parametric estimation of Lévy processes (with C. Houdré). In IMS Lecture Notes-Monograph Series (LNMS). High Dimensional Probability IV. IMS Lecture Notes (editors: E. Gine, V. Kolchinskii, W. Li, J. Zinn). Volume 51, 96-116, 2006. DOI:10.1214/074921706000000789


• On the asymptotic redundancy of lossless block coding with two codeword lengths (with C. Houdré). IEEE Transactions on Information Theory, 688-692, Vol. 51, 2005. DOI:10.1109/TIT.2004.840858.
  
  

• Some Preprints and current work:


• Small-time expansions for local jump-diffusions models with infinite jump activity (with Cheng Ouyang). This version: September 2011. Submitted


• High-order short-time expansions for ATM option prices under the CGMY model (with Ruoting Gong and Christian Houdré). This version: December 2011. Submitted.


• Nonparametric regression with rescaled time series errors (with Michael Levine). This version: January 2012. Submitted.


• The large-time smile and skew for exponential Lévy model (with Martin Forde and Antoine Jacquier). This version: February 2012. Submitted.


• Small-time asymptotics of stopped Lévy bridges and simulation schemes with controlled bias (with Peter Tankov). This version: March 2012. Submitted.

• Other manuscripts:


• An overview of a nonparametric estimation method for Levy processes (with C. Houdre).


• A selected survey of portfolio optimization problems.

Other professional activities:

• Associate Editor, Electronic Journal of Statistics.
• Co-organizer of the Conference Modeling High Frequency Data in Finance 3 at Stevens Institute of Technology, July 27-31, 2011.
• Co-organizer of the Special Session on Stochastic processes with applications to mathematical finance at the AMS 2011 Central Section Meeting to be held in Iowa City, IA, March 18-20, 2011
• Co-organizer of the Special Session on Financial mathematics and statistics at the Spring AMS Southeastern Section Meeting, University of Kentucky, March 27-28, 2010.

Curriculum Vitae. (This version: March 2012).

Recent or upcoming conferences:

• SIAM Conference on Financial Mathematics and Engineering. Minneapolis, MN, July 9-11, 2012.
• XII Latin American Congress of Probability and Mathematical Statistics. Vina del Mar, Chile, March 26-30, 2012.
• Informs 2011 Annual Meeting. Charlotte, NC, November 13-16, 2011.
• High Dimensional Probability. Banff International Research Station for Mathematical Innovation and Discovery. Canada, October 9-14, 2011.

Talks:

• Small-time asymptotics of stopped Levy bridges and simulation schemes with controlled bias, CLAPEM 2012, Vinia del Mar, Chile, March 30, 2012.
• Dynamic Portfolio Optimization with a Defaultable Security and Regime Switching, INFORMS, Charlotte, NC, Nov. 14, 2011.
• Option Pricing under Regime-Switching, ECE Seminar, Purdue University, Nov. 9, 2011.
• Small-time expansions for local jump-diffusions models with infinite-jump activity, High-Dimensional Probability, BIRS Canada, Oct. 10, 2011.
• Small-time expansions for local jump-diffusions models, Probability Seminar, Purdue University, Oct. 4, 2011.
• Near-expiration option prices in Levy financial models, ICIAM, Vancouver, CA, July 20, 2011.
• Central limit theorems for the nonparametric estimation of time-changed Levy models. Statistics and Modeling for Complex Data. Session: Statistics for finance. Ecole des Ponts Paris-Tech, France, June 22-24, 2011.
• Near-expiration behavior of implied volatility for exponential Levy models. Risk Seminar, Statistics Department, Columbia University, Spring 2011.
• Near-expiration behavior of implied volatility for exponential Levy models. Financial Mathematics Seminar, The Stevanovich Center for Financial Mathematics, The University of Chicago, Spring 2011.
• Near-expiration behavior of implied volatility for exponential L\'evy models . SIAM-SEAS Minisymposium in Mathemtical Finance (UNC, Charlotte) and Central Sectional AMS Meeting (Iowa), Spring 2011.
• On the small-maturity behavior of implied volatilities under exponential Levy models. Computational Finance Seminar, Purdue, Spring 2011.
• Small-time asymptotics for Levy processes and their application to estimation and option pricing . Bachelier seminar, France, Fall 2010.
• High-Frequency based estimation of exponential Levy Models. Indiana University Statistics Colloquium, Fall 2010.
• Small-time statistical behavior of Levy processes and its application to the estimation and pricing of Levy-based financial models. Seminar on Mathematical Finance and Financial Engineering. Georgia Tech. Department of Mathematics. Fall 2010.
• Optimal portfolios and admissible strategies in a Levy-driven markets . International Workshop in Applied Probability, Universidad Carlos III de Madrid, Summer 2010.
• High-Frequency based estimation of exponential L\'evy Models. Modeling High Frequency Data in Finance II, Stevens Institute of Technology, Summer 2010.
• Mini course on "Statistical Methods for Financial Models driven by Levy Processes." Lecture 1, Lecture 2, Lecture 3, Lecture 4. The Pan-American Advanced Studies Institute, CIMAT, Mexico, Summer 2010.
• Nonparametric estimation for a Time-changed Levy Model. Southeastern Sectional AMS Meeting, Spring 2010.

• Nonparametric estimation for a Time-changed Levy Model. Mathematics Colloquium, University of Louisville, Spring 2010.

• Nonparametric estimation for a Time-changed Levy Model. Research Colloquium, Purdue University, Spring 2010.

• Accurate asset price modeling and related statistical problems under microstructure noise. VIGRE Seminar, Purdue University, Fall 2009.

• Nonparametric estimation of time-changed L\'evy models. Applied Mathematics Colloquia, Illinois Institute of Technology, November 2009. Also presented at the Mathematical Finance and Probability Seminar, Rutgers University, October 2009.

• Optimal portfolios and admissible strategies in a Levy market Stochastic Analysis at Purdue '09 Workshop 2009.

• Some estimation problems related to time-changed L\'evy models. Mathematical statistics seminar. Department of Statistics. Purdue University.

• Sieve-based confidence intervals and bands for Levy densities. Mathematical statistics seminar. Department of Statistics. Purdue University.

• Non-parametric methods for L\'evy-based financial models. Workshop on Infinitely Divisible Processes. CIMAT. Guanajuato, Mexico. March 2009.

• Modeling and estimating the dynamics of asset prices. VIGRE Seminar, Purdue University, Fall 2008.

• Model selection for Levy processes based on discrete-sampling. The fifth international conference on High Dimensional Probabilty. CIRM, Luminy, France. May, 2008.

• State-dependent utility maximization in markets driven by additive Levy processes . AMS Spring Central Section Meeting, Bloomington, IN. Special Session on Financial Mathematics, April, 2008.

• State-dependent utility maximization in Levy markets. Seminar on Mathematical Finance and Financial Engineering. Georgia Tech. Department of Mathematics. Spring 2008.

• Introduction to pricing methods for credit derivatives. Computationa Finance Seminar, Purdue University, Spring 2008.

• Modeling and estimation of the dynamics of asset prices. VIGRE Seminar, Purdue University, Fall 2007.

• Model selection for Levy processes based on discrete-sampling . Statistics Research Colloquium, Purdue University, Fall 2007.

• Non-parametric estimation for some models driven by Levy processes,The Third Erich L. Lehmann Symposium, 2007.

• State-dependent utility maximization in Levy markets, Kent-Purdue Mini Symposium on Financial Mathematics, 2007

• State-dependent utility maximization in Levy markets, Probability and statistics seminar, USC, Feb. 2007.

• Notes, Seminar "Topics in Financial Mathematics", UCSB, Jan. 2007.

• Calibration and portfolio optimization issues in asset price modelling driven by Levy processes, ORIE Colloquium, Cornell, Jan. 2007.

• Estimation Methods for Levy based models of asset prices, Financial Mathematics Seminar, Statistics Department, UCSB, Oct. 2006
  • Slides Talk 1
  • Slides Talk 2
  • Notes

• Nonparametric methods for financial models driven by Levy processes, Special Colloquium, Department of Statistics, Purdue University, Mar. 2006

The content of this page and any opinions expressed therein are solely those of Jose E. Figueroa-Lopez.

Last modified: April 2012