Economic recoveries can be slow, fast, or involve double dips. This paper provides an explanation based on the dynamic interactions between bank lending standards and firm entry selection. Recoveries are slower when high-quality borrowers postpone their investments, which occurs if the borrower pool has lower quality on average. Double dips can occur when banks endogenously produce information, which increases waiting benefits discontinuously. The model is consistent with both aggregate- and industry-level data.

I develop a theory to jointly explain several coincident long-term trends in the United States — increased usage of intangible capital, growth and compositional shifts in the financial sector, and higher income inequality. Active finance intermediates intangible, high-risk capital by monitoring its use, whereas tangible, low-risk capital is intermediated passively. If new firms are more productive but feature less tangible or riskier assets, the model endogenously generates the aforementioned trends. Inequality is a key source of feedback effects in the model: active finance, which relies on contributions from wealthy individuals, becomes more cost-effective as inequality rises. A similar story emerges if technological progress occurs directly in the financial sector (e.g., financial innovation). I discuss several of the model’s auxiliary predictions and their potential to be consistent with the data.

The results discussed in the talk are joint with F. Viens and X. Zhang (Purdue University). The talk is devoted to uncorrelated Gaussian stochastic volatility models. The volatility of an asset in such a model is described by the absolute value of a Gaussian process. We find sharp asymptotic formulas with error estimates for the realized volatility and the asset price density in a general Gaussian model, and also characterize the wing behavior of the implied volatility. For Gaussian models with self-similar volatility processes, we obtain sharp asymptotic formulas describing the small-time behavior of the asset price density, the call pricing function, and the implied volatility. The parameters appearing in the asymptotic formulas mentioned above are expressed in terms of the Karhunen-Loeve characteristics of the volatility process.
We will discuss numerous examples of Gaussian and self-similar stochastic volatility models, and show how to recover the self-similarity index knowing the small-time behavior of the call pricing function or the implied volatility.

When a stock’s price follows a local volatility model, Peter Carr observed the convex duality relationship between the price of a contingent claim and the value of the delta-hedging portfolio when the payoff of the contingent claim is convex, which leads to significant additional insight in the relationship among the stock dynamics, the delta-hedging process, the value process of the contingent claim and the cash borrowed for constructing the hedging portfolio.

The financial innovations in the past several decades have lead to the creation of many new types of financial derivatives. They become increasingly liquid and, thus, can also be used as hedging devices. It turns out, when hedging a target contingent claim using another hedging claim, a similar relationship also emerges between the value of the target contingent claim and value of the hedging portfolio in terms of generalized duality.

In this talk we explore the ramification of this generalized duality. In particular, the preservation of the generalized convexity of the target contingent claim’s payoff and its various applications.

This is a joint research with Dr. Peter Carr.

We propose a new class of unit root tests that exploits invariance properties in the Locally  Asymptotically  Brownian  Functional  limiting  experiment  of  the  unit  root model. These invariance structures naturally suggest tests based on the ranks of the increments of the observations, their mean, and an assumed reference density for the innovations. The tests are semiparametric in the sense that the reference density need not equal the true innovation density. For correctly speci^Led reference density, the asymptotic power curve of our test is point-optimal and nearly exploitscient (in the sense of Elliott, Rothenberg, and Stock (1996). When using a Gaussian reference density, our test performs as well as commonly used tests under true Gaussian innovations and better under other distributions, e.g., fat-tailed or skewed. Monte Carlo evidence shows that our test also behaves well in small samples.

We develop econometric tools for studying jump dependence of two processes from high-frequency observations on a fixed time interval. In this context, only segments of data around a few outlying observations are informative for the inference.  We derive an asymptotically valid test for stability of a linear jump relation over regions of the jump size domain. The test has power against general forms of nonlinearity in the jump dependence as well as temporal instabilities. We further propose an optimal estimator for the linear jump regression model that is formed by optimally weighting the detected jumps with weights based on the diffusive volatility around the jump times. We derive the asymptotic limit of the estimator, a semiparametric lower efficiency bound for the linear jump regression, and show that our estimator attains the latter. The analysis covers both deterministic and random jump arrivals. A higher-order asymptotic expansion for the optimal estimator further allows for finite-sample refinements. In an empirical application, we use the developed inference techniques to test the stability (in time and jump size) of market jump betas.

We propose a test for the rank of a cross-section of processes at a set of jump events. The jump events are either specific known times or are random and associated with jumps of some process. The test is formed from discretely sampled data on a fixed time interval with asymptotically shrinking mesh. In the first step, we form nonparametric estimates of the jump events via thresholding techniques. We then compute the eigenvalues of the outer product of the cross-section of increments at the identified jump events. The test for rank $r$ is based on the asymptotic behavior of the sum of the squared eigenvalues excluding the largest $r$. A simple resampling method is proposed for feasible testing.

The test is applied to financial data spanning the period 2007-2015 at the times of stock market jumps. We find support for a one-factor model of both industry portfolio and Dow 30 stock returns at market jump times. This stands in contrast with earlier evidence for higher-dimensional factor structure of stock returns during “normal” (non-jump) times. We identify the latent factor driving the stocks and portfolios as the size of the market jump. (WIth Jia Li and Viktor Todorov.)

Recent research has documented the existence of common factors in individual asset’s idiosyncratic variances or squared idiosyncratic returns. We provide an Arbitrage Pricing Theory that leads to a linear factor structure for prices of squared excess returns. This pricing representation allows us to study the interplay of factors at the return level with those in idiosyncratic variances. We document the presence of a common volatility factors. Linear returns do not have exposure to this factor when using at least five principal components as linear factors. The price of the common volatility factor is zero. (With
Thijs van der Heijden, and Bas J.M. Werker.)