Alec Kercheval

Research and Students

Research Areas

My research at FSU has focused on financial mathematics and mathematical economics, including portfolio and credit risk modeling, high frequency analysis of the limit order book, and, jointly with Paul Beaumont, agent-based modeling of asset pricing dynamics. Current projects include:

Macroeconomic asset pricing models and Agent-based dynamics. We are studying the out-of-equilibrium dynamics of markets with learning agents in a Lucas framework of asset pricing. This work is motivated by the need to understand market dynamics like high price volatility and pricing bubbles, which are not explained by traditional equilibrium theory.
Credit risk, portfolio risk, and jump dependence. Most financial random variables are not Normal. This is particularly true for default related derivatives, such as basket credit default swaps (CDS): extreme events are more common than predicted by the normal distribution, and "default contagion" means that firms are more likely to default after others already have. Correlated Levy processes can be used to price basket CDS, and to model risk for portfolios of assets with jumps.
High frequency limit order book dynamics. High-frequency trading is becoming dominant in financial markets, where intra-day matters such as order book dynamics become important. We are looking at models of order-book dynamics via generalized birth-death processes as a framework for high-frequency trading strategies.

Current and Former PhD Students

Hubeyb Gurdogan, PhD candidate, Levy processes, portfolio optimization.
Heting Yan, PhD Spring 2020, machine learning and the limit order book. Placement: Microsoft.
Navid Salehy, PhD Spring 2019, Random walks over point processes and their application in finance; placement: Department of Mathematics, University of New Orleans.
Chenchen Zhou, PhD Summer 2017, On the multidimensional default threshold model for credit risk; placement: Wells Fargo, NC.
Yuanda Chen, PhD Spring 2017, Modeling the limit order book using Hawkes processes; placement: Goldman Sachs, NY.
Chun-Yuan Chiu, PhD Fall 2016, Modeling credit risk in the default threshold framework; placement: Bank of America Merrill Lynch, NY
Dawna Jones, PhD Summer 2015 FSU (Asset pricing equilibria for heterogeneous, limited information agents, co-directed with Paul Beaumont): placement: Wells Fargo, Charlotte, NC.
Pierre Garreau, PhD Fall 2013 FSU (Jump dependence and multidimensional defaul risk: a new class of structural models with stochastic intensities); placement: Deutsche Bank, Jacksonville, FL.
Yuan Zhang, PhD Fall 2013 FSU (Modeling high frequency order book dynamics with support vector machines); placement: Yahoo!, Sunnyvale, CA.
Henry Huang, PhD Spring 2012 FSU (Modeling Order Book Processes Using Queues and Point Processes); placement: Quant, AllianceBernstein, NYC.
Yang Liu, PhD Spring 2012 FSU (Risk Forecasting and Portfolio Optimization with GARCH, Skewed t Distributions, and Multiple Timescales); placement: Quant, Florida State Board of Administration, Tallahassee.
Tianyu Liang, PhD Spring 2012, FSU (Alternative Models for Stochastic Volatility Corrections for Equity and Interest Rate Derivatives, co-directed with Xiaoming Wang); placement: Quantitative Derivatives Analyst, ING, Philadelphia.
Michelle Guan, PhD Summer 2011 FSU (Asset Market Dynamics of Heterogeneous Agent Models with Learning, co-directed with Paul Beaumont); placement: Assistant Professor, Department of Mathematics and Actuarial Science, Indiana University Northwest
Juan Moreno, PhD Fall 2007 FSU (Impulse control problems under non-constant volatility); placement: Quant, Investment Board of Wisconsin.
Andrew Culham, PhD Summer 2007 FSU (Asset pricing in a Lucas framework with boundedly rational, heterogeneous agents, co-directed with Paul Beaumont); placement: Quantitative Analyst, Florida Power and Light. Dissertation: [pdf]
Jianke Zhang, PhD Spring 2007 FSU (Numerical methods for portfolio risk estimation); placement: Quantitative Analyst, Florida Power and Light
Wenbo Hu, PhD Fall 2005 FSU (Calibration of multivariate generalized hyperbolic distributions using the EM algorithm, with applications in risk management, portfolio optimization, and portfolio credit risk); placement: Quant, Bell Trading, Chicago.
Brian Tandy, PhD 1997 UT Austin (Cantor sets and Lipschitz actions on circles and trees); placement: Digeo Corp., Palo Alto
Paul Fabel, PhD 1994 UT Austin (Self-homeomorphisms of the 2-sphere which pointwise fix a nonseparating continuum); placement: Assistant Professor, Dept. of Mathematics, Mississippi State University

Selected Publications

Books

Lectures on Financial Mathematics: Discrete Asset Pricing (with G. Anderson), Synthesis Lectures on Mathematics and Statistics, Morgan and Claypool, 2010.

Selected Articles

Links go to PDF preprints.

Modeling credit risk in the jump threshold framework (with C.-Y. Chiu), Applied Mathematical Finance, 2018, DOI: 10.1080/1350486X.2018.1465349, 23 pages.
A structural jump threshold framework for credit risk (with P. Garreau), SIAM Journal on Financial Mathematics, vol. 7, no. 1, 2016, 642-673.
Modeling high-frequency limit order book dynamics with support vector machines (with Y. Zhang), Quantitative Finance, vol 15, no 8, 2015, 1315--1329.
Complex Dynamics in Equilibrium Asset Pricing Models with Boundedly Rational, Heterogeneous Agents (with P. Beaumont and Y. Guan), Complexity, vol 19, no 3, 2014, 38--55.
Asset Market Dynamics in Equilibrium Models with Heterogeneous Agents: Analytical Results (with P. Beaumont and A. Culham), Advances in Economics and Business, vol 1, no 2, 2013, 49-56.
A generalized birth-death stochastic model for high-frequency order book dynamics (with H. Huang), Quantitative Finance, vol 12, no. 4, 2012, 547-557.
Risk Forecasting with GARCH, Skewed t Distributions, and Multiple Timescales (with Y. Liu), chapter 7 in Handbook of Modeling High-Frequency Data in Finance, J. Wiley, 2012, 163-218.
Portfolio optimization for t and skewed t returns (with W. Hu), Quantitative Finance, vol 10, no 1, 2010, 91-105.
The Skewed t distribution for portfolio credit risk (with W. Hu), Advances in Econometrics, vol 22, Elsevier, 2009, 55-83.
On Rebonato and Jackel's parametrization method for finding nearest correlation matrices, International Journal of Pure and Applied Mathematics, vol 45, no 3, 2008, 383-390.
Risk Management with Generalized Hyperbolic Distributions (with W. Hu), Proceedings of the Fourth IASTED International Conference on Financial Engineering and Applications, ACTA Press, Calgary, (2007), 19 -- 24.
Optimal covariances in risk model aggregation, Proceedings of the Third IASTED International Conference on Financial Engineering and Applications, ACTA Press, Calgary, (2006) 30--35.
On the Aggregation of Local Risk Models for Global Risk Management (with G. Anderson, L. Goldberg, G. Miller, and K. Sorge), Journal of Risk, 8, no. 1 (2005) 25--40.
t-Statistics for Weighted Means in Credit Risk Modelling (with L. Goldberg and K. Lee), Journal of Risk Finance, 6, no. 4 (2005) 349--365.
Modelling credit risk: currency dependence in global credit markets (with L. Goldberg and L. Breger), J. Portfolio Management, vol 29, no. 2, Winter 2003. Abstract.
Denjoy minimal sets are far from affine, Ergodic Th. and Dyn. Systems, vol 22 (2002), 1803--1812. Erratum, arXiv:1004.1363v1 [math.DS] (2010), 1 page.
Cantor sets, binary trees, and Lipschitz circle homeomorphisms (with B. Tandy), Michigan Math. J., vol. 46 (1999) 29-38.
Denjoy's Theorem with Exponents, Proc. Amer. Math. Soc., vol 127, no. 10 (1999) 3111-3118.
Wandering domains and invariant conformal structures for mappings of the 2-torus (with D. Sullivan), Ann. Acad. Sci. Fenn., Series A I Math., vol. 21 (1996) 51-68.
On sets of critical values in the real line (with S. Bates), Duke Math. J., vol. 83, (1996), 399-413.
The Zygmund Morse-Sard Theorem, Journal of Geometric Analysis, 4, No.3 (1994) 403-424.
The Gauss-Green theorem for fractal boundaries (with J. Harrison), Duke Math. J., 67 (1992), 575-588.
A $C^{1\times \infty}$ function with an interval of critical values, Indiana Univ. Math. J., 40, No.4 (1991), 1483-1488.
Geometric integration on fractal curves in the plane (with J. Harrison), Indiana Univ. Math. J., 40, No.2 (1991), 567-594.
Critical sets in the plane (with C. Pugh), Mich. Math. J. 38 (1991), 441-459.
An area approach to wandering domains for smooth surface endomorphisms, Ergod. Theory and Dyn. Sys. 11 (1991), 181-187.
Functions not constant on fractal quasi-arcs of critical points, Proc. Amer. Math. Soc., 106 (1989), 397-406.
Continued fractions and differentiability of functions, Amer. Math. Monthly, 95 (1988), 639-643.
A critical set with non-null image has large Hausdorff dimension, Trans. Amer. Math. Soc., 296 (1986), 367-376.

Alec Kercheval

Research and Students

Research Areas

Current and Former PhD Students

Selected Publications

Books

Selected Articles

Seminars and Conferences

Teaching

Links to other activity at FSU

Contact