|
Probability
and Statistics in Complex Systems: Genomics, Networks, and Financial
Engineering, September 1, 2003 - June 30, 2004
Abstracts:
IMA
Workshop:
May
24-28, 2004
Photo
Gallery Material
from Talks
Luca
Benzoni
(Finance Department, University of Minnesota) lbenzoni@umn.edu
http://legacy.csom.umn.edu/WWWPages/FACULTY/lbenzoni/
Stochastic
Volatility, Mean Drift, and Jumps in the Short-Term Interest
Rate (poster session)
Joint
work with Torben G. Andersen (Northwestern
University) and Jesper Lund (Nykredit
Bank).
We
find that an intuitively appealing and fairly manageable continuous-time
model provides an excellent characterization of the U.S. short-term
interest rate over the post Second World War period. Our three-factor
jump-diffusion model consists of elements embodied in existing
specifications, but our approach appears to be the first to
successfully accommodate all such features jointly. Moreover,
we conduct simu ltaneous and efficient inference regarding all
model components, which include a shock to the interest rate
process itself, a time-varying mean reversion factor, a stochastic
volatility factor and a jump process. Most intriguingly, we
find that the restrictions implied by an affine representation
of the jump-diffusion system are not rejected by the U.S. short
rate data. This allows for a tractable setting for a ssociated
asset pricing applications.
Kent
D. Daniel (Kellogg School of Management, Northwestern
University) kentd@kellogg.northwestern.edu
http://kent.kellogg.nwu.edu/
Testing
Factor-Model Explanations of Market Anomalies
A number of recent papers have attempted to explain the size
and book-to-market anomalies with either (1) factor models based
on economically motivated factors, or (2) with conditional CAPM
or CCAPM models with economically motivated conditioning variables.
These papers use similar methodologies and similar test assets,
and generally fail to reject the proposed models. We argue that
these tests may fail to reject because of low statistical power
of the tests against reasonable alternative hypotheses, rather
than because the models are consistent with the data. We propose
an alternative test methodology with higher power against the
proposed alternatives, and show that the new test methodology
results in the rejection of several of the proposed factor models
at high levels of significance.
Michael
A.H. Dempster
(Centre for Financial Research, Judge Institute of Management,
University of Cambridge & Cambridge Systems Associates Limited)
m.dempster@jims.cam.ac.uk
Modelling
the Global FX Market
Slides:
html
pdf
ps
ppt
This
talk reports on work undertaken with the support of HSBC to
understand the $1.4 B per day global currency market. After
a general introduction, the detailed structure of the global
FX market will be described with a focus on the roles of the
major market makers and the EBS and Reuters 3000 electronic
interdealer markets. Next modelling individual agents, traders
and market makers with computational learning techniques based
on extensive quote, trade, agent order flow and order book data
seen by a market maker will be reported. Finally, work in progress
to construct realistic agent simulation models of the essence
of the global market will be discussed which attempts to capture
the current mechanisms of price discovery - at least over intervals
shorter than those at which macroeconomic fundamentals are thought
to dominate market movements.
Gregory
R. Duffee
(Haas School of Business, University of California-Berkeley)
duffee@haas.berkeley.edu
http://faculty.haas.berkeley.edu/duffee/
A
No-Arbitrage Term Structure Model Without Latent Factors
Slides: pdf
Paper: pdf
I
present a framework for modeling part of the dynamics of the
term structure. The framework can be used to link the term structure
to observed variables such as inflation and output. Its partial
nature allows us to dispense with yield-based factors (e.g.,
latent factors) while retaining restrictions associated with
no-arbitrage. I apply the model to the joint dynamics of inflation
and the term structure. As other research has noted, both short-term
and long-term bond yields adjust gradually to a change in inflation.
I find that the dynamics of the price of interest rate risk
needed to fit this pattern from 1983 through 2003 are implausible.
An alternative interpretation is that investors were systematically
surprised by the slow adjustment of short-term yields to inflation.
Philip
H. Dybvig (Olin School of Business, Washington
University in Saint Louis) pdybvig@dybfin.wustl.edu
Exploration
of Interest Data
Slides:
pdf
Absent unreasonably strong assumptions, financial theory places
almost no restriction on interest rates and bond prices. If
the short rate process exists (not even an implication of most
preferences we study), then bond and interest derivative prices
are given by expected discounted values using the rolled-over
spot rate for discounting and risk-neutral ("martingale'')
probabilities for computing expectations. Absent theoretical
guidance, the choice of interest rate process should ideally
be dictated by the data. This presentation explores the interest-rate
process starting with the sample version of the quadratic variation
of the three-year Treasury Bill discount process, using about
50 years worth of daily data from the Fed's H15 tape. This analysis
updates an analysis done in 1990 with an eye toward looking
at the impact of what seems to be a unique regulatory and economic
environment today, but the major conclusions are unchanged.
A final comment relates the analysis to a result on parameter
uncertainty from a FAJ paper with Bill Marshall.
J.
Doyne Farmer (Santa
Fe Institute) jdf@santafe.edu
http://www.santafe.edu/~jdf
Modeling
Liquidity, Risk and Transaction Costs in the London Stock Exchange
Using Low Intelligence Agents
Slides:
html
pdf
ps
ppt
I
will present a variety of empirical results based on a study
of the London Stock Exchange. The data set contains about 350M
events, including every action by every trader on every stock,
making it possible to reconstruct the limit order book at any
instant in time. This study has generated a variety of new empirical
results, including a characterization of the approximate power
law behavior and long-memory effects associated with price returns,
order placement, and the spread. My collaborators and I have
shown that price changes are largely driven by fluctuations
in liquidity. A model for order flow is developed, that when
simulated along with its impact on prices, explains many of
statistical properties of the data very well. Finally, time
permitting, I will present some preliminary results developing
an agent ecology of arbitraguers who exploit liquidity demanders,
and discuss their affect on prices. These results illustrate
first, that there are many strong regularities in market behavior
at the microstructure level, and second, that many aspects of
these regularities can be understood based on what might be
characterized as low intelligence models of agent behavior.
Dean
P. Foster (University of Pennsylvania, The Wharton
School) foster@gosset.wharton.upenn.edu
http://gosset.wharton.upenn.edu/~foster/
Ponzironi: The Search for Statistically Significant
Excess Returns
Slides:
pdf
ps
Joint
work with Robert A. Stine.
Almost
everyone you talk to claims to have a scheme that "beats the
market." How should we test such claims? We created a test (based
on Bennett's inequality) that only assumes that CAPM excess
returns should be martingale. But the claimants scoff at our
test and say that it doesn't have sufficient power to show the
beauty of their scheme.
With
tongue firmly in cheek, we will provide a few schemes that will
pass any weakening of our test. This has been a wonderful teaching
aid, since the schemes are understandable to MBAs. Finally we
will revisit Fama and French's book to market ratio as a way
of generating excess returns and ask does it have enough jump
to pass our statistical test.
Xavier
Gabaix
(Department of Economics, Massachusetts Institute of Technology)
xgabaix@mit.edu http://econ-www.mit.edu/faculty/xgabaix/papers.htm
A
Theory of Power Law Distributions in Financial Market Fluctuations
Papers: NatureMay2003Published.pdf
cubicfeb16-20041.pdf
Joint
work with Parameswaran Gopikrishnan,
Vasiliki Plerou, and H.
Eugene Stanley (Center for Polymer Studies and Department
of Physics, Boston University).
Insights
into the dynamics of a complex system are often gained by focusing
on large fluctuations. For the financial system huge databases
now exist which facilitates the analysis of large fluctuations
and the characterization of their statistical behavior [1,2].
Power laws appear to describe histograms of relevant financial
fluctuations, such as fluctuations in stock price, trading volume,
and the number of trades [3-10]. Remarkably, the exponents that
characterize these power laws are similar for different types
and sizes of markets, for different market trends, and even
for different countries - suggesting that a generic theoretical
basis may underlie these phenomena. Based on a plausible set
of assumptions, we propose a model that provides an explanation
for these empirical power laws. In addition, our model explains
certain striking empirical regularities that describe the relationship
between large fluctuations in prices, trading volume, and the
number of trades. In our model, large movements in stock market
activity arise from the trades of the large participants. Starting
from an empirical characterization of the size distribution
of large market participants (mutual funds), we show that their
trading behavior when performed in an optimal way, generates
power-laws observed in financial data.
Rohitha
Goonatilake
(Department of Mathematical and Physical Sciences, Texas A&M
International University) harag@tamiu.edu
Development,
Evaluation and Analysis of a 20-Year Deferred Annuity Product
(poster session)
Report:
pdf
This
project analyzes an annuity product that suits the needs of
today's American family under moderate assumptions. It helps
in the study of the pricing accuracy in a mutual life insurance
company and to better understand the extent of the analysis
and computations involved in developing a 20-year deferred annuity
product designed for a group of 1000 people; ages ranging from
30 - 40 years and having a 5 year old child.
Lars
Peter Hansen
(Department of Economics University of Chicago) l-hansen@uchicago.edu
http://home.uchicago.edu/~lhansen/
Recursive
Robust Control and Prediction
Slides:
pdf
When
confronting a stochastic environment, a decision-maker may not
have full confidence in his probabilistic assignments and may
not observe the full array state variables that characterize
the probabilistic model. Instead he or she may wish to explore
how decision rules perform when the stochastic specification
is altered or perturbed. In this paper we consider decision
problems in which a class of such perturbations are permitted.
By introducing these perturbations, decision rules for prediction
and control are made to be more robust. We develop and explore
recursive formulations of the robust control/prediction problem
and deduce corresponding risk-sensitive recursions that feature
a distinct risk-adjustment for predicting the hidden Markov
states.
Joint
with Marco Cagetti, Thomas
J. Sargent and Noah Williams.
Narasimhan
Jegadeesh (Emory University) Narasimhan_Jegadeesh@bus.emory.edu
Value
of Analyst Recommendations: International Evidence*
Slides:
html pdf
ps
ppt
Paper:
pdf
Joint
work with Woojin Kim.
This
paper examines analyst recommendations in the G7 countries and
evaluates the value of these recommendations over the 1993 to
2002 period. We find that the frequencies of sell and strong
sell recommendations in all countries are far less than that
of buy and strong buy recommendations. The frequency of sell
recommendations is the lowest in the U.S. We also find that
stock prices react significantly to recommendation revisions
on the revision day and on the following day in all of these
countries except Italy. We find the largest price reactions
in the U.S., followed by Japan. We also evaluate trading strategies
that buy upgraded stocks and sell downgraded stocks. Here again,
we find the highest profits in the U.S., followed by Japan.
*
Narasimhan Jegadeesh
is the Dean's Distinguished Professor at the Goizueta Business
School, Emory University, and Woojin Kim is a doctoral student
at the University of Illinois at Urbana-Champaign. We would
like to thank Cliff Green and Michael Weisbach, and the seminar
participants at Duke University, the University of Alabama at
Tuscaloosa, the University of Illinois at Urbana-Champaign,
and Vanderbilt University for helpful comments. We are responsible
for any errors.
Contact information: Narasimhan Jegadeesh, Goizueta Business
School, 1300 Clifton Road, Atlanta, GA 30322, email: Narasimhan.Jegadeesh@bus.emory.edu;
Woojin Kim, 340, Wohlers Hall, University of Illinois at Urbana-Champaign,
Champaign, IL 61820, email: wkim5@uiuc.edu.
Steven
Kou (Department of Industrial Engineering and
Operations Research (IEOR), Columbia University Columbia University)
sk75@columbia.edu http://www.columbia.edu/~sk75/
A Tale of Two Growths: Modeling Stochastic Endogenous
Growth and Growth Stocks
This paper extends the deterministic endogenous R&D growth model
to a stochastic endogenous growth model, which is used to study
growth stocks. The model provides an understanding of the links
between economic growth, monopolistic competition in R&D, and
the valuation of growth stocks. With the presence of stochastic
shocks, the model leads to a decomposition of the value of growth
stocks. The decomposition implies that the value of growth stocks
should be very volatile, while the long-run average return is
roughly equal to the growth rate of R&D labor. The model also
explains an empirical size distribution puzzle observed for
the cross-sectional study of growth stocks.
Vladimir
Kurenok
(Department of Natural and Applied Sciences, University of Wisconsin-Green
Bay)
On
a Model for the Term Structure of Interest Rate Processes of
Stable Type (poster session)
Nick
Laskin
(IsoTrace Lab, Department of Physics, University of Toronto)
nick.laskin@utoronto.ca
Jump
Dynamics and Stochastic Volatility for Stock Returns
(poster session)
We
develop approach to model components of return distribution,
which are assumed to be led by a news arrival random process.
It is assumed that the compound generalized Poisson process
governs information arrivals. The compound generalized Poisson
process captures long-memory effect, which results in non-exponential
distribution of interarrival times. The conditional variance
of returns is decomposed into two components, a smoothly evolving
component for standard diffusion of past news impacts and the
component related to the information arrival process that generates
jump stream with fractional statistics. The developed model
predicts impact of large changes in stock returns on volatility.
Empirical evidence of the impact jump versus normal return innovations
and time-series of jump clustering has been presented.
Kiseop
Lee
(Department of Mathematics, University of Louisville) kiseop.lee@louisville.edu
Estimation
of Liquidity Risk by Multiple Change-Point Models (poster
session)
Liquidity
risk is often defined as the additional risk in the market due
to the timing and size of a trade. Based on a pioneering work
of Cetin et al. we develop an estimation method which is practically
of use. Our new method estimates liquidity cost by applying
a sequential multiple change-point detection algorithm to a
broken-line regression model.
Ding
Li (Department of Economics and Finance, Northern
State University) Ding.Li@northern.edu
Empirical
Study of Investment Behavior in Equity Markets Using Wavelet
Methods (poster session)
This
empirical study addresses stock returns behavior using wavelet
methods in time-scale domain. Financial markets data revealed
more complex dynamic patterns than random walk, the objective
of this study is to apply scale analysis to explore the scale-dependent
property of stock returns behavior to support the reference-dependence
theory in behavioral finance. In this research, we study eleven
years of daily returns for three hundred stocks sampled from
the S&P 1500 index. The sample data is further categorized into
groups according to their market capitalizations, divided into
three time periods, and wavelet decomposed at level six. Our
findings support the reference-dependence argument. We find
patterns that stock returns statistical properties are scale-dependent.
Our results show that stock returns are non-normally distributed
and nonstationary at small scales but normal and stationary
at relatively larger scales. We find significant market effects
on individual assets and mixed results on different stock caps.
Also stock returns cannot always be modeled as long memory processes.
Our results support that people associate different investment
horizons with different mental accounts.
Juyoung
Lim
(Department of Mathematics, The University of Texas at Austin)
limju@math.utexas.edu
An
Application of Large Deviation Principle to Pricing Multi Asset
Derivative Securities (poster
session)
Poster:
pdf
Paper: pdf
Joint
work with M. Avellaneda.
We
present a statistical method to estimate conditional expectation
of multivariate diffusion process in short time horizon. The
result includes asymptotic convergence theorem for estimator
and its standard error that is based on Large Deviation Principle.
Quantities from multivariate diffusion process are often analytically
intractable and this method gives an effective method to estimate
them without simulation and offers a way to undertand its risk
profile intuitively.
An
application is demonstrated with relative value pricing of multi
asset derivatives such as index option and swaption.
Jun
Liu (Finance Group Anderson Graduate School
of Management, University of California-Los Angeles) jliu@anderson.ucla.edu
http://www.personal.anderson.ucla.edu/jun.liu/
Information,
Diversificiation, and Cost of Capital
We
study the pricing implications of information in a noisy rational
expectations model with a factor structure for multi-asset payoffs.
There are two classes of price taking investors in our model;
informed investors who receive private signals on systematic
and idiosyncratic components of asset payoffs, and uninformed
investors who draw imperfect inferences about those signals
from prices. We solve the equilibrium explicitly. We show that
only information about systematic factors matters in determining
asset risk premiums, when the number of the risky assets is
large. Idiosyncratic risk as well as the information associated
with them is fully diversifiable.
Jun
Liu (Finance Group Anderson Graduate School
of Management, University of California-Los Angeles) jliu@anderson.ucla.edu
http://www.personal.anderson.ucla.edu/jun.liu/
Risk,
Return and Dividends (poster
session)
Paper:
pdf
Joint
work with Andrew Ang (Columbia
University and NBER).
We
characterize the joint dynamics of expected returns, stochastic
volatility, and prices. In particular, with a given dividend
process, one of the processes of the expected return, the stock
volatility, or the price-dividend ratio fully determines the
other two. For example, the stock volatility determines the
expected return and the price-dividend ratio. By parameterizing
one, or more, of expected returns, volatility, or prices, common
empirical specifications place strong implicit, and sometimes
inconsistent, restrictions on the dynamics of the other variables.
Our results are useful for understanding the risk-return trade-off,
as well as the predictability of stock returns.
Jun
Pan
(MIT Sloan School of Management, ) junpan@mit.edu
http://www.mit.edu/~junpan
The
Information in Option Volume for Future Stock Prices
Paper: pdf
Joint
work with Allen M. Poteshman (University
of Illinois at Urbana-Champaign).
We
find strong evidence that option trading volume contains information
about future stock price movements. Taking advantage of a unique
dataset from the Chicago Board Options Exchange, we construct
put to call ratios for underlying stocks, using volume initiated
by buyers to open new option positions. Performing daily crosssectional
analyses from 1990 to 2001, we find that buying stocks with
low put/call ratios and selling stocks with high put/call ratios
generates an expected return of 40 basis points per day and
1 percent per week. This result is present during each year
of our sample period, and is not affected by the exclusion of
earnings announcement windows. Moreover, the result is stronger
for smaller stocks, indicating more informed trading in options
on stocks with less efficient information flow. Our analysis
also sheds light on the type of investors behind the informed
option trading. Specifically, we find that option trading from
customers of full service brokers provides the strongest predictability,
while that from firm proprietary traders is not informative.
Finally, in contrast to the equity option market, we do not
find any evidence of informed trading in the index option market.
Monika
Piazzesi (Graduate School of Business, University
of Chicago) mpiazzes@gsb.uchicago.edu
http://gsbwww.uchicago.edu/fac/monika.piazzesi/research/
Futures
Prices as Risk-Adjusted Forecasts of Monetary Policy
Slides:
pdf
Many
researchers have used federal funds futures rates as measures
of financial markets' expectations of future monetary policy.
However, to the extent that federal funds futures reflect risk
premia, these measures require some adjustment for risk premia.
In this paper, we document that excess returns on federal funds
futures have been positive on average. We also document that
expected excess returns are strongly countercyclical. In particular,
excess returns are surprisingly predictable by employment growth
and other business-cycle indicators such as Treasury yields
and corporate bond spreads. Excess returns on eurodollar futures
display similar patterns. We document that simply ignoring these
risk premia has important consequences for the future expected
path of monetary policy. We also investigate whether risk premia
matter for conventional measures of monetary policy surprises.
Michael
Tehranchi
(Department of Mathematics, University of Texas at Austin) tehranch@math.utexas.edu
Optimal
Portfolio Choice in Bond Markets (poster
session)
We
consider the Merton problem of optimal portfolio choice when
the traded instruments are the set of zero-coupon bonds. Working
within an infinite-factor Markovian Heath-Jarrow-Morton model
of the interest rate term structure, we find conditions for
the existence and uniqueness of optimal trading strategies.
When there is uniqueness, we provide a characterization of the
optimal porfolio.
Ruey
S. Tsay
(Graduate School of Business, University of Chicago) ruey.tsay@gsb.uchicago.edu
Efficient
Estimation of Stochastic Diffusion Models with Leverage Effects
and Jumps
Slides:
pdf
Paper:
pdf
This
talk is concerned with estimating stochastic diffusion models
with leverage effects and with or without jumps. Several methods
have been proposed in the literature to estimate such models
including efficient method of moments (EMM) and Markov chain
Monte Carlo (MCMC) method. For MCMC methods, most of the existing
methods cannot deal with leverage effects or require intensive
computation. We discuss the difficulties of the estimation problem
and propose a modified method that can estimate the model efficiently.
Simulation and real examples are used to compare estimation
results of various methods.
Diane
Louise Wilcox
(Department of Mathematics and Applied Mathematics, University
of Cape Town) diane@maths.uct.ac.za
Periodicity
and Scaling of Eigenmodes in an Emerging Market (poster
session)
Joint
work with Tim Gebbie.
We
investigate periodic, aperiodic and scaling behaviour of eigenmodes,
i.e. daily price fluctuation time-series derived from eigenvectors,
of correlation matrices of shares listed on the Johannesburg
Stock Exchange (JSE) from January 1993 to December 2002. Periodic,
or calendar, components are investigated by spectral analysis.
We demonstrate that calendar effects are limited to eigenmodes
which correspond to eigenvalues outside the Wishart range. Aperiodic
and scaling behaviour of the eigenmodes are investigated by
using rescaled-range methods and detrended fluctuation analysis
(DFA). We find that the eigenmodes which correspond to eigenvalues
within the Wishart range are dominated by noise effects. In
particular, we find that interpolating missing data or illiquid
trading days with a zero-order hold introduces high frequency
noise and leads to the overestimation of uncorrected (for serial
correlation) Hurst exponents. DFA exponents of the eigenmodes
suggest an absence of long-term memory.
Shu
Wu
(Department of Economics, The University of Kansas) shuwu@ku.edu
Interest
Rate Risk and the Forward Premium Anomaly in Foreign Exchange
Markets (poster session)
premiums
implied by the yield curves across countries, uncovered interest
rate parity (UIP) is still strongly rejected by the data. Moreover,
factors that predict the excess bond returns are found not significant
at all in predicting the foreign exchange returns. These results
reject the joint restrictions on the exchange rate and interest
rates imposed by dynamic term structure models, suggesting that
foreign exchange markets and bond markets may not be fully integrated
and we have to look beyond interest rate risk in order to understand
the exchange rate anomaly.
Yong
Zeng
(Department of Mathematics and Statistics, University of Missouri
at Kansas City) zeng@mendota.umkc.edu
Filtering
with a Marked Point Process Observation: Applications to the Econometrics
of Ultra-High-Frequency Data (poster
session)
Slides:
pdf
ps
Ultra-high-frequency
(UHF) data are naturally modeled as a marked point process (MPP),
because of the random arrival times as well as the associated
marks such as price, volume and ask and bid quotes at an arrival
time. Even though econometricians model UHF data as a MPP, they
view UHF data as an irregularly-spaced time series. Here, we
take the angle of probabilists and view UHF data as an observed
sample path of a marked point process (MPP). Then, we propose
a general filtering model for UHF data where the signals are
latent processes with time-varying parameters and the observations
are in a generic mark space with other observable factors. The
latent process and parameters are jointly modeled by a martingale
problem and the observable factors are allowed in the stochastic
intensity kernel of the MPP. In this way, we obtain a unified
framework for many existing models for UHF data.
The
powerful tools of stochastic filtering are introduced for developing
the statistical foundations of the proposed model. The likelihoods,
posterior, likelihood ratios and Bayes factors, are studied.
They all are of continuous time, of infinite dimension and are
characterized by stochastic differential equations such as filtering
equations. To calculate, for example, likelihoods or posterior
of a proposed model, consistent algorithms are required. Mathematical
foundations for consistent, efficient algorithms are established.
There are two general approaches for constructing recursive
algorithms. One approach is Kushner's Markov chain approximation
method, and the other is Sequential Monte Carlo method
or particle filtering method. The latter approach is
more attractive in that it can mitigate and even avoid the ``curse
of dimensionality'' in complex models. Especially, Bayesian
inference (estimation and model selection) via filtering are
developed for the proposed model.
Photo
Gallery Material
from Talks
Probability
and Statistics in Complex Systems: Genomics, Networks, and Financial
Engineering, September 1, 2003 - June 30, 2004
|
