2007-2008 FINANCIAL MATHEMATICS SEMINAR

Unless otherwise noted, the seminars take place on 4:30 pm on Friday, in Room 133 of Eckhart Hall.

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Open to the public.

More speakers will be added over time. The listed speakers are confirmed unless otherwise noted.

Date	Speaker	Affiliation	Title of Talk (click for abstract)
10/5/2007	Wolfgang Polonik	University of California, Davis	Nonparametric Testing for Multivariate Volatility Models
10/11/2007 Eckhart 110 9:30-10:30 am	Asger Lunde	Aarhus School of Business, Denmark	Bipower Variation with Noisy Data (PDF)
10/19-20/2007		Stevanovich Center 2007 Conference on Credit Risk
11/2/2007	Yazhen Wang	University of Connecticut	Modeling and Analyzing High-Frequency Financial Data
11/9/2007 downtown 2nd Friday on Finance	Andrew Lo	Laboratory for Financial Engineering, MIT	What happened to the quants in August 2007
11/16/2007	Alexander Lindner	Technische Universit�t M�nchen, University of Marburg, and University of Braunschweig, Germany	A continuous time GARCH process driven by a Levy process
11/30/2007	Amil Dasgupta	London School of Economics	The Price Impact of Institutional Herding
12/7-8/2007		Conference in Honor of Stanley Pliska (arranged by UIC and IIT)
12/10/2007 Monday 4:30 pm Eckhart 110	Dale Rosenthal	The University of Chicago	Trade Signing and Nearly-Gamma Random Variables
12/12/2007 Wednesday 4:30 pm Eckhart 110	Ilze Kalnina	London School of Economics	Subsamplig High Frequency Data
12/14/2007 Friday 4:30 pm Eckhart 110	Mathieu Rosenbaum	Universite Paris-Est	Integrated Volatility and Round-off Error
1/11/2008 downtown 2nd Friday on Finance	Nassim Taleb		From Practice to Theory, the Origins of Model Error: Preasymptotics and Inverse Problems in Quantitative Finance
2/22/2008	Stathis Tompaidis	University of Texas	Pricing American-Style Options by Monte Carlo Simulation: Alternatives to Ordinary Least Squares
4/4/2008	Qiwei Yao	London School of Economics	Analysing Time Series with Nonstationarity: Common Factors and Curve Series
4/10/2007		One Day Workshop on Finance and Statistics
4/11/2008 downtown 2nd Friday on Finance	Kenneth Singleton	Stanford University	Why Do Risk Premiums in Sovereign Credit Markets Covary?
4/18/2008	Mathieu Kessler	Universidad Politecnica de Cartagena, Spain	Exact filters for discretized diffusions
4/23/2008 CAMP Seminar 4:00pm, Eckhart 202	Ronnie Sircar	Princeton University	Convex Risk Measures in Financial Mathematics
THURSDAY 4/24/2008 4:15pm, Ryerson 251	Ronnie Sircar	Princeton University	Homogeneous Groups and Multiscale Intensity Models for Multiname Credit Derivatives
4/25/2008	Dag Tjostheim	University of Bergen, Norway	Estimation in time series that are both nonlinear and nonstationary
5/2/2008	Jianqing Fan	Princeton University	Modeling and Estimation of High-Dimensional Covariance Matrix for Portfolio Allocation and Risk Management
5/9/2008	Jostein Paulsen	University of Bergen and University of Chicago	Optimal dividend payments and reinvestments of diffusion processes with both fixed and proportional costs
5/16/2008	Richard Thaler	The University of Chicago	TBA
5/30/2008	Sebastian Jaimungal	University of Toronto	TBA
6/6/2008	Matheus Grasselli	McMaster University	TBA

ABSTRACTS

Nonparametric Testing for Multivariate Volatility Models: Wolfgang Polonik; Department of Statistics; University of California, Davis; A novel nonparametric methodology is presented that facilitates the investigation of different features of a volatility function. We will discuss the construction of tests for (i) heteroscedasticity, for (ii) a bathtub shape, or a "smile effect", and (iii) a parametric volatility model, where interestingly the resulting test for a smile effect can be viewed as a nonparametric generalization of the well-known LR-test for constant volatility versus an ARCH model. The tests can also be viewed as tests for the presence of certain stochastic dominance relations between two multivariate distributions. The inference based on those tests may be further enhanced through associated diagnostic plots. We will illustrated our methods via simulations and applications to real financial data. The large sample behavior of our test statistics is also investigated.

This is joint work with Q. Yao, London School of Economics.
Modeling and Analyzing High-Frequency Financial Data: Yazhen Wang; National Science Foundation and University of Connecticut; Volatilities of asset returns are central to the theory and practice of asset pricing, portfolio allocation, and risk management. In financialeconomics, there is extensive research on modeling and forecastingvolatility based on Black-Scholes, diffusion, GARCH, stochastic volatilitymodels and option pricing formulas. Nowadays, thanks to technologicalinnovations, high-frequency financial data are available for a host ofdifferent financial instruments on markets of all locations and at scaleslike individual bids to buy and sell, and the full distribution of suchbids. The availability of high-frequency data stimulates an upsurgeinterest in statistical research on better estimation of volatility. Thistalk will start with a review on low-frequency financial time series andhigh-frequency financial data. Then I will introduce popular realizedvolatility computed from high-frequency financial data and present my workon wavelet methods for analyzing jump and volatility variations and thematrix factor model for handling large size volatility matrices. Theproposed wavelet based methodology can cope with both jumps in the priceand market microstructure noise in the data, and estimate both volatilityand jump variations from the noisy data. The matrix factor model isproposed to produce good estimators of large size volatility matrices byattacking non-synchronized problem in high-frequency price data and reducing the huge dimension (or size) of volatility matrices. Parts of mytalk are based on joint work with Jianqing Fan, Qiwei Yao, and Pengfei Li.
What happened to the quants in August 2007: Amir E. Khandani and Andrew W. Lo; MIT; During the week of August 6, 2007, a number of high-profile and highlysuccessful quantitative long/short equity hedge funds experiencedunprecedented losses. Based on empirical results from TASS hedge-fund dataas well as the simulated performance of a specific long/short equitystrategy, we hypothesize that the losses were initiated by the rapidunwinding of one or more sizable quantitative equity market-neutralportfolios. Given the speed and price impact with which this occurred, itwas likely the result of a sudden liquidation by a multi-strategy fund orproprietary-trading desk, possibly due to margin calls or a riskreduction. These initial losses then put pressure on a broader set oflong/short and long-only equity portfolios, causing further losses onAugust 9th by triggering stop-loss and de-leveraging policies. Asignificant rebound of these strategies occurred on August 10th, which isalso consistent with the sudden liquidation hypothesis. This hypothesissuggests that the quantitative nature of the losing strategies wasincidental, and the main driver of the losses in August 2007 was thefiresale liquidation of similar portfolios that happened to bequantitatively constructed. The fact that the source of dislocation inlong/short equity portfolios seems to lie elsewhere---apparently in acompletely unrelated set of markets and instruments---suggests thatsystemic risk in the hedge-fund industry may have increased in recentyears.
A continuous time GARCH process driven by a Levy process: Alexander Lindner; Technische Universit�t M�nchen, University of Marburg, and University of B raunschweig, Germany; A continuous time GARCH process which is driven by a Levy process is introduced. It is shown that this process shares many features with the discrete time GARCH process. In particular, the stationary distribution has heavy tails. Extensions of this process are also discussed. We then turn attention to some first estimation methods for this process, with particular emphasis on a generalized method of moment estimator. Finally, we also report on how the continuous time GARCH process approximates discrete time GARCH processes, when sampled at discrete times. The talk is based on joint work with Stephan Haug (TU Munich), Claudia Klueppelberg (TU Munich) and Ross Maller (Australian National University).
The Price Impact of Institutional Herding: Amil Dasgupta; London School of Economics and CEPR; We present a simple theoretical model of the price impact of institutional herding. In our model, career-concerned fund managers interact with profit-motivated proprietary traders and monopolistic market makers in a pure dealer-market. The reputational concerns of fund managers generate endogenous conformism, which, in turn, impacts the prices of the assets they trade. In contrast, proprietary traders trade in a contrarian manner. We show that, in markets dominated by fund managers, assets persistently bought (sold) by fund managers trade at prices that are too high (low) and thus experience negative (positive) long-term returns, after uncertainty is resolved. The pattern of equilibrium trade is also consistent with increasing (decreasing) short-term transaction- price paths during or immediately after an institutional buy (sell) sequence. Our results provide a simple and stylized framework within which to interpret the empirical literature on the price impact of institutional herding. In addition, our paper generates several new testable implications. (Joint with with Andrea Prat and Mechela Verardo)
Signing and Nearly-Gamma Random Variables: Dale Rosenthal; University of Chicago; Many financial events involve delays. I consider data delays and propose metrics for other phenomena: the mean time to deletion from a financial index, the weighted-average prepayment time for a loan portfolio, and the weighted-average default time for a loan portfolio. Under reasonable conditions, these are all nearly-gamma distributed; thus various small-sample approximations are examined. This approach also yields a metric of loan portfolio diversity similar to one used in rating collateralized debt obligations. Finally, the approximations are used to create a model for signing trades. The model is flexible enough to encompass the midpoint, tick, and EMO methods and yields probabilities of correct predictions.
Pricing American-Style Options by Monte Carlo Simulation: Alternatives to Ordinary Least Squares: Stathis Tompaidis; University of Texas; We investigate the performance of the Ordinary Least Squares (OLS) regression method in Monte Carlo simulation algorithms for pricing American options. We compare OLS regression against several alternatives and find that OLS regression underperforms methods that penalize the size of coefficient estimates. The degree of underperformance of OLS regression is greater when the number of simulation paths is small, when the number of functions in the approximation scheme is large, when European option prices are included in the approximation scheme, and when the number of exercise opportunities is large. Based on our findings, instead of using OLS regression we recommend an alternative method based on a modification of Matching Projection Pursuit. (Joint with Chunyu Yang)
Analysing Time Series with Nonstationarity: Common Factors and Curve Series: Qiwei Yao; London School of Economics; We introduce two methods for modelling time series exhibiting nonstationarity. The first method is in the form of the conventional factor model. However the estimation is carried out via expanding the white noise space step by step, therefore solving a high-dimensional optimization problem by many low-dimensional sub-problems. More significantly it allows the common factors to be nonstationary. Asymptotic properties of the estimation were investigated. The proposed methodology was illustrated with both simulated and real data sets. The second approach is to accommodate some nonstationary features into a stationary curved (or functional) time series framework. It turns that the stationarity, though defined in a Hilbert space, facilitates the estimation for the dimension of the curved series in terms of a standard eigenanalysis.
Estimation in time series that are both nonlinear and nonstationary: Dag Tjostheim; University of Bergen; Motivated by problems in nonlinear cointegration theory I will look at estimation in time series that are both nonlinear and nonstationary. The models considered are nonlinear generalizations of the random walk. Markov recurrence theory is used to establish asymptotic distributions. The emphasis is on nonparametric estimation, but I will also look at parametric estimation in a nonstationary threshold model.
Homogeneous Groups and Multiscale Intensity Models for Multiname Credit Derivatives: Ronnie Sircar; Princeton University; The pricing of basket credit derivatives is contingent upon
1. realistic modeling of the firms' default times and the correlation between them; and
2. efficient computational methods for computing the portfolio loss distribution from the firms' marginal default time distributions.
We revisit intensity-based models and, with the aforementioned issues in mind, we propose improvements
1. via incorporating fast mean-reverting stochastic volatility in the default intensity processes; and
2. by considering a hybrid of a top-down and a bottom-up model with homogeneous groups within the original set of firms.
We present a calibration example from CDO data, and discuss the relative performance of the approach.
This is joint work with Evan Papageorgiou.
Modeling and Estimation of High-Dimensional Covariance Matrix for Portfolio Allocation and Risk Management: Jianqing Fan; Princeton University; Large dimensionality comparable to the sample size is a common feature as in modern portfolio allocation and risk management. Motivated by the Capital Asset Pricing Model, we propose to use a multi-factor model to reduce the dimensionality and to estimate the covariance matrix among those assets. Under some basic assumptions, we have established the rate of convergence and asymptotic normality for the proposed covariance matrix estimator. We identify the situations under which the factor approach can gain substantially the performance and the cases where the gains are only marginal, where compared with covariance matrix. We also introduce the concept of sparse portfolio allocation and propose two efficient algorithms for selecting the optimal subset of the portfolio. The risk of the optimally selected portfolio is thoroughly studied and examined. The performance, in terms of risk and utility, of the sparsely selected portfolio is compared with the classical optimal portfolio of Markowitz (1952).
Optimal dividend payments and reinvestments of diffusion processes with both fixed and proportional costs: Jostein Paulsen; University of Bergen and University of Chicago; Assets are assumed to follow a diffusion process subject to some conditions. The owners can pay dividends at their discretion, but whenever assets reach zero, they have to reinvest money so that assets never go negative. With each dividend payment there is a fixed and a proportional cost, and so with reinvestments. The goal is to maximize expected value of discounted net cash flow, i.e. dividends paid minus reinvestments. It is shown that there can be two different solutions depending on the model parameters and the costs.
1. Whenever assets reach a barrier they are reduced by a fixed amount through a dividend payment, and whenever they reach 0 they are increased to another fixed amount by a reinvestment.
2. There is no optimal policy, but the value function is approximated by policies of the form described in Item 1 for increasing barriers. We provide criteria to decide whether an optimal solution exists, and when not, show how to calculate the value function. It is discussed how the problem can be solved numerically and numerial examples are given. The talk is based on a paper with the same title to appear in SIAM Journal of Control and Optimization.

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