Seminars for 2020-2022

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Monday, November 28, 2022, 10:45-11:45 am
Stevanovich Center Library (5727 South University Avenue) 

Uwe Schmock

Professor for Financial and Actuarial Mathematics, Vienna University of Technology

Modelling and Aggregation of Dependent Risks

The stochastic modelling and aggregation of dependent risks is a central risk management task  for many financial institutions. After an introduction illustrating some basic mathematical challenges, we will review Poisson approximation, the collective model from actuarial science, Panjer distributions, and the extended multivariate Panjer recursion. To assure numerical stability, we introduce weighted convolutions combined with the Panjer recursion, thereby widening the class of mixture distributions. The aim is to discuss a multi-business-line variant of the collective model, mixed by a convex combination of non-negative (mainly unbounded) claim number intensities to obtain an arbitrary linear dependence structure — and still use recursive methods to calculate the loss distribution of the portfolio.

Time permitting, an implementation will be presented, which is available online

Thursday, April 28, 2022 – 11am-12pm noon- Virtual 

Jeroen Dalderop

Assistant Professor of Economics, University of Notre Dame, IN

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Efficient Estimation of Pricing Kernels and Market-Implied Densities
This paper studies the nonparametric identification and estimation of projected pricing kernels implicit in European option prices and underlying asset returns using conditional moment restrictions. The proposed series estimator avoids computing ratios of estimated risk-neutral and physical densities. Instead, we consider efficient estimation based on the conditional Euclidean empirical likelihood or continuously-updated GMM criterion, which takes into account the informativeness of option prices of varying strike prices beyond observed conditioning variables. In a second step, we convert the implied probabilities into predictive densities by matching the informative part of cross-sections of option prices. Empirically, pricing kernels tend to be U-shaped in the S&P 500 index return given high levels of the VIX, and call and ATM options are more informative about their payoff than put and OTM options.

Monday, May 17, 2021 – 4pm-5pm – Virtual – In partnership with the University of Chicago Department of Statistics

Markus Reiß

Professor for Mathematical Statistics, Humboldt-Universität zu Berlin

Zoom Link

Testing the Rank of Time-varying Covariance Matrices
We consider the instaneous (or spot) covariance matrix $\Sigma(t)$ of a multidimensional martingale of the form $dX(t)=\Sigma(t)^{1/2}dB(t)$, $B$ a Brownian motion. The data is given by high-frequency observations of $X$ on a fixed time interval. We test the null hypothesis $H_0$ that $\rank(\Sigma(t))\le r$ for all $t$ against the alternative $\lambda_{r+1}(\Sigma(t))\ge v_n$ that the $r+1$st eigenvalue is larger than some separation rate $v_n$. This problem can be embedded in Ingster’s nonparametric signal detection framework, but it has many unexpected features. For instance, the optimal detection rate v_n depends on a regularity assumption on $\Sigma(t)$ under the null, not the alternative and a possible spectral gap leads to significantly better detection rates. The proofs rely on perturbation and  deviation inequalities for random matrices which might have independent interest. Further results under observational noise will be discussed and applications to intraday bond markets will be presented.
(joint work with Lars Winkelmann, Berlin)

Thursday, February 18, 2021 (was previously scheduled for 2/11) – 11am-noon – Virtual 

Jian Li

Ph D student in the joint Economics and Finance program, University of Chicago, IL. Jian won a 2020 Stevanovich Fellowship Award.

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The Importance of Investor Heterogeneity: An Examination of the Corporate Bond Market

Corporate bond market participants are increasingly worried about liquidity. However, bid-ask spreads and other standard measures indicate liquidity has not deteriorated significantly. This paper proposes a potential reconciliation. We show credit yields became four times more sensitive to bid-ask spreads in 2019 than in 2005. We then provide a model that connects this change to the rapid growth of mutual funds in the corporate bond market. The model features heterogeneous investors with different trading needs who choose between a risk-free asset and illiquid bonds. As the risk-free rate declines, more short-term investors reach for yield and enter the bond market. These short-term investors reduce the selling pressure in each sub-market and so the bid-ask spreads. However, their greater trading needs amplify the sensitivity of credit yields to the bid-ask spreads, leading to a larger liquidity component. We next test the model’s predictions using detailed data on investor holdings in the U.S. As predicted, we find investor turnover amplifies the effect of illiquidity on credit yields. Bonds with more short-term investors are traded at lower bid-ask spreads and their credit yields are more sensitive to the bid-ask spreads. Finally, we look across countries and show that, consistent with the model, larger declines in risk-free rates are associated with higher growth in mutual fund shares. These results highlight the key role that investor heterogeneity plays in determining corporate bond yields and ultimately firms’ financing conditions.

Thursday, February 4, 2021 – 11am-noon – Virtual

Rui Da

Ph D Candidate in Econometrics, Chicago Booth School of Business, University of Chicago, IL. Rui won a 2020 Stevanovich Fellowship award.

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The Statistical Limits of Arbitrage

We relax the absence of near-arbitrage bound by recognizing the statistical limits to arbitrage — the ignorance of population parameters in linear asset pricing models. We then classify the new maximal arbitrage-free space by the strength and sparsity of alphas. Standard statistical methods that are designed for identifying potentially strong alphas miss vast investment opportunities of the weaker ones. We propose a new approach to construction of portfolios that optimally exploit both strong alphas and weaker ones. We demonstrate how individually impotent alphas can collectively lead to large investment gains. For illustration we construct optimal portfolios with large-cap US stocks, for which strong investment opportunities are less obvious, and our approach leads to a substantial 50% gain in Sharpe ratios compared to widely used alternatives.

Thursday, January 14, 2021 – 1:30pm-2:30pm – Virtual – In partnership with the Econometrics and Statistics Colloquium (ESC) in Booth School of Business

Yoosoon Chang

Professor of Economics, Indiana University in Bloomington, IN

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Identifying and Estimating the Longrun Effect of Income Distribution on Aggregate Consumption

Permanent components of income and  consumption are obtained by functional Beveridge-Nelson decomposition of U.S. Consumer Expenditure Survey data. From the permanent income distribution, we identify two factors the level (aggregate) and the spread (redistribution) that affect permanent consumption. Longrun consumption is most positively affected by households with monthly earnings of around $2,000, households with lower income have negative effects on aggregate consumption, and those with $5,000 or more respond little to income redistribution. Limited income sharing across households, high entry barriers, and nontrivial adjustment costs associated with both human and physical capital accumulation may contribute to the empirical findings. Taking the estimated longrun response function as the optimal behavior of households, counterfactual taxation exercises suggest that purely redistributive policies can increase the permanent component of aggregate consumption by 250%.