#### Contingent Capital, Tail Risk, and Debt-Induced Collapse (Review of Financial Studies, July 2017)

**(joint with Nan Chen, Paul Glasserman and Behzad Nouri)**

Contingent capital in the form of debt that converts to equity as a bank approaches financial distress offers a potential solution to the problem of banks that are too big to fail. This paper studies the design of contingent convertible bonds and their incentive effects in a structural model with endogenous default, debt rollover, and tail risk in the form of downward jumps in asset value. We show that once a firm issues contingent convertibles, the shareholders’ optimal bankruptcy boundary can be at one of two levels: a lower level with a lower default risk or a higher level at which default precedes conversion. An increase in the firm’s total debt load can move the firm from the first regime to the second, a phenomenon we call debt-induced collapse because it is accompanied by a sharp drop in equity value. We show that setting the contractual trigger for conversion sufficiently high avoids this hazard. With this condition in place, we investigate the effect of contingent capital and debt maturity on capital structure, debt overhang, and asset substitution. We also calibrate the model to past data on the largest U.S. bank holding companies to see what impact contingent convertible debt might have had under the conditions of the financial crisis.

#### State-Varying Factor Models of Large Dimensions **(March 2018)**

**(joint with Ruoxuan Xiong)**

This paper develops an inferential theory for state-varying factor models of large dimensions. Unlike constant factor models, loadings are general functions of some recurrent state process. We develop an estimator for the latent factors and state-varying loadings under a large cross-section and time dimension. Our estimator combines nonparametric methods with principal component analysis. We derive the rate of convergence and limiting normal distribution for the factors, loadings and common components. In addition, we develop a statistical test for a change in the factor structure in different states. Applying the estimator to U.S. Treasury security data, we find that the systematic factor structure differs in times of booms and recessions as well as in periods of high market volatility.

#### Sure Profits via Flash Strategies and the Impossibility of Predictable Jumps **(January 2018)**

**(joint with Claudio Fontana and Eckhard Platen)**

In an arbitrage-free financial market, asset prices should not exhibit jumps of a predictable magnitude at predictable times. We provide a rigorous formulation of this result in a fully general setting, only allowing for buy-and-hold positions and without imposing any semimartingale restriction. We show that asset prices do not exhibit predictable jumps if and only if there is no possibility of obtaining sure profits via high-frequency limits of buy-and-hold trading strategies. Our results imply that, under minimal assumptions, price changes occurring at scheduled dates should only be due to unanticipated information releases.

#### Large-Dimensional Factor Modeling Based on High-Frequency Observations **(November 2017)**

This paper develops a statistical theory to estimate an unknown factor structure based on financial high-frequency data. I derive a new estimator for the number of factors and derive consistent and asymptotically mixed-normal estimators of the loadings and factors under the assumption of a large number of cross-sectional and high-frequency observations. The estimation approach can separate factors for normal “continuous” and rare jump risk. The estimators for the loadings and factors are based on the principal component analysis of the quadratic covariation matrix. The estimator for the number of factors uses a perturbed eigenvalue ratio statistic. The results are obtained under general conditions, that allow for a very rich class of stochastic processes and for serial and cross-sectional correlation in the idiosyncratic components.

#### Understanding Systematic Risk: A High-Frequency Approach **(January 2017)**

Under a large dimensional approximate factor model for asset returns, I use high-frequency data for the S&P 500 firms to estimate the latent continuous and jump factors. I estimate four very persistent continuous systematic factors for 2007 to 2012 and three from 2003 to 2006. These four continuous factors can be approximated very well by a market, an oil, a finance and an electricity portfolio. The value, size and momentum factors play no significant role in explaining these factors. For the time period 2003 to 2006 the finance factor seems to disappear. There exists only one persistent jump factor, namely a market jump factor. Using implied volatilities from option price data, I analyze the systematic factor structure of the volatilities. There is only one persistent market volatility factor, while during the financial crisis an additional temporary banking volatility factor appears. Based on the estimated factors, I can decompose the leverage effect, i.e. the correlation of the asset return with its volatility, into a systematic and an idiosyncratic component. The negative leverage effect is mainly driven by the systematic component, while it can be non-existent for idiosyncratic risk.

#### Contingent Convertible Bonds: Pricing, Dilution Costs and Efficient Regulation **(May 2012)**

This paper develops and compares different modeling approaches for contingent capital with tail risk, debt rollover and endogenous default. In order to apply contingent convertible capital in practice it is desirable to base the conversion on observable market prices that can constantly adjust to new information in contrast to accounting triggers. I show how to use credit spreads and the risk premium of credit default swaps to construct the conversion trigger and to evaluate the contracts under this specification.

#### How Relative Compensation can lead to Herding Behavior (**January 2017)**

**(joint with An Chen)**

In this paper we analyze performance-based remuneration for risk- averse managers in a Black-Scholes-type model. We assume that the firm’s performance is influenced by an industry and a firm-specific risk. A relative performance compensation which rewards a manager relative to the exogenous performance of the firms in his peer group, can filter out the industry-specific risk and lower the compensation costs to the firm. However, if all managers of the firms in the peer group receive an endogenous relative performance compensation, we show that the managers may herd in their investment decisions and choose an inferior investment despite the presence of a more profitable alternative. This herding behavior is mainly driven by the managers’ risk-aversion and the endogenous relative performance compensation.

#### Optimal Stock Option Schemes for Managers (**Review of Managerial Science, ****June 2013)**

**(joint with An Chen) **

This paper analyzes which stock option scheme best aligns the interests of a firm's manager and shareholders when both are risk-averse. We consider granting to the manager a basic fixed salary and one of the following four options: European, Parisian, Asian and American options. Choosing the strike of the options optimally, the shareholders can mostly implement a first best solution with all payoff schemes. The American option scheme best aligns the interests of the manager and the shareholders in the most common case in which the strike price equals the grant-date fair market value.

#### New Performance-Vested Stock Option Schemes (**Applied Financial Economics, January 2013)**

**(joint with An Chen and Klaus Sandmann)**

In the present paper, we analyze two effective non-traditional performance-based stock option schemes which we call Parisian and constrained Asian executives' stock option plans. Both options have a criterion on the terminal value similar to a call option, but in addition impose a restriction on the path of the firm's assets process. Under a Parisian option scheme, the bonus of the executives becomes effective when the stock price has outperformed a certain threshold for a fixed length of time. Under the constrained Asian scheme, the executives' compensation is coupled with the average performance of the stock price. We show that the value of both ESO schemes are less sensitive to changes in risk than plain vanilla options and hence represent an alternative compensation scheme that could make exaggerated risk taking through the executives less likely.