This paper presents new models for the dependence structure, or copula, of economic variables based on a factor structure.  The proposed models are particularly attractive for high dimensional applications, involving fifty or more variables.  This class of models generally lacks a closed-form density, but analytical results for the implied tail dependence can be obtained using extreme value theory, and estimation via a simulation-based method using rank statistics is simple and fast.  We study the finite-sample properties of the estimation method for applications involving up to 100 variables, and apply the model to daily returns on all 100 constituents of the S&P 100 index. We find
significant evidence of tail dependence, heterogeneous dependence, and asymmetric dependence, with dependence being stronger in crashes than in booms.  We also show that the proposed factor copula model provides superior estimates of some measures of systemic risk.

We propose and illustrate a Markov-switching multi-fractal duration (MSMD) model for analysis of inter-trade durations in financial markets.  MSMD is a parameter-driven long-memory model of conditional intensity dynamics, with long memory driven by structural Markov-switching components.  The popular standard ACD duration model neglects all of those features.  A few other notable duration models have featured them in isolation or in smaller assemblies, but none have featured them all.  MSMD does so in a simple and parsimonious fashion, successfully capturing the key features of financial market inter-trade durations: long-memory dynamics and over-dispersed distributions.  Empirical exploration suggests MSMD’s superiority relative to the leading competitor. (With F. Chen and F. Schorfheide)

Both practitioners and academics have come to use the implied volatility surface to represent information in options contracts.  This paper proposes a new framework for analyzing volatility risk and risk premium directly on the volatility surface.  First, instead of specifying the instantaneous variance rate dynamics as in the standard literature, we specify the implied volatility dynamics, and derive dynamic no-arbitrage implications directly on the shape of the implied volatility surface.  Under several candidate dynamics specifications, the shape of the implied volatility can be cast as solutions to a simple quadratic equation, dramatically simpler than the numerical integration or Fourier inversion involved in even the most tractable stochastic volatility models in the literature.  Second, corresponding to each implied volatility, we propose a new realized volatility measure specific to that strike and maturity, so that the delta-hedged gains from holding this option can be directly computed as the difference between the new realized volatility measure and the corresponding implied volatility.  The difference between the expected value of the newly defined realized volatility surface and the implied volatility surface measures the volatility risk premium embedded in each option contract.  Estimating different implied and realized variance dynamics to the two volatility surfaces show that even though the square-root variance dynamics is the most popular in the option pricing literature, the data support more of a log-normal dynamics. Under this specification, we extract volatility risk and volatility risk premiums from the two volatility surfaces, and find that both the extracted volatility risk premiums and the extracted stochastic volatility skew can significantly predict future stock returns, with the forecasting R-squared estimates significantly higher than those reported in the literature.

This work was motivated by a problem that arises in algorithmic trading, of designing a trading strategy to buy or sell a given amount of a stock in a day at an average price that closely matches the volume-weighted-average-price (VWAP) of the stock throughout the day.  VWAP is commonly used by institutional investors such as pension funds and mutual funds as a benchmark.  VWAP orders are available through most brokerage houses and are seen as a way to reduce execution costs.  Recently NASDAQ has filed an application with the Securities and Exchange Commission to introduce their own VWAP order; proceedings regarding the application have been initiated.  We study the problem of designing a trading strategy to match VWAP in a model where price and volume dynamics are co-dependent.  Using dynamic programming we are able to provide a closed-form formula for the optimal trading strategy in the absence of market impact.  We provide empirical evidence for the effectiveness of the strategy for the 30 stocks that form the Dow Jones index.  We also study the performance and effectiveness of the proposed strategy in the setting where there trading causes both temporary and permanent price impact.  Joint with Jedrzej Bialkowski (University of Canterbury) and Daniel Mitchell (University of Texas at Austin)

The modern theory of option pricing rests on It\^{o} calculus, which is a second order calculus based on the quadratic variation of a stochastic process. One can instead develop a first order stochastic calculus, which is based on the running minimum of a stochastic process, rather than its quadratic variation. We focus here on the analog of geometric Brownian motion (GBM) in this alternative stochastic calculus. The resulting stochastic process is a positive continuous martingale whose laws are easy to calculate. We show that this analog behaves locally like a GBM whenever its running minimum decreases, but behaves locally like an arithmetic Brownian motion otherwise. We provide closed form valuation formulas for vanilla and barrier options written on this process. We also develop a reflection principle for the process and use it to show how a barrier option on this process can be hedged by a static position in vanilla options.

High-frequency realized variance approaches offer great promise for estimating asset prices’ covariation, but encounter difficulties connected to the Epps effect.  This paper models the Epps effect in a stochastic volatility setting.  It adds dependent noise to a factor representation of prices. The noise both offsets covariation and describes plausible lags in information transmission.  Non-synchronous trading, another recognized source of the effect, is not required.  A resulting estimator of correlations and betas performs well on LSE mid-quote data, lending empirical credence to the approach.

Covariance structure is of fundamental importance in many areas of statistical inference and a wide range of applications, including genomics, fMRI analysis, risk management, and web search problems.  In the high dimensional setting where the dimension p can be much larger than the sample size n, classical methods and results based on fixed p and large n are no longer applicable.  In this talk, I will discuss some recent results on optimal estimation of large covariance and precision matrices.  The results and technical analysis reveal new features that are quite different from the conventional low-dimensional problems.  Time permitting, I will also discuss sparse linear discriminant analysis with high-dimensional data.

The talk begins with a short discussion on the nature of corporate default prediction and the elements required of a good default prediction model, and move on to cover two parts.  First, a family of dynamic models based on doubly stochastic Poisson processes is introduced as a device to relate common risk factors and individual attributes to observed defaults while handling the censoring effect arising from other forms of firm exit such as mergers and acquisitions.  I will describe two implementation frameworks based on spot intensity (Duffie, Saita and Wang, 2007, Journal of Financial Economics) and forward intensity (Duan, Sun and Wang, 2012, Journal of Econometrics), respectively.  The discussions will cover their conceptual foundations, econometric formulations, implementation issues and empirical findings using the US corporate data.  The talk will also touch upon the role of momentum in default prediction and on how to measure distance-to-default for financial firms.  I will argue in favor of the forward intensity method because it is easily scalable for practical applications that inevitably deal with a large number of firms and many covariates.
The talk moves on to the Credit Research Initiative (CRI) that was launched by the Risk Management Institute of National University of Singapore in July 2009 in response to the 2008-09 global financial crisis.  Its corporate default prediction system is currently powered by a forward intensity model to produce daily updated and freely accessible term structure of default probabilities (up to 5 years) on over 60,000 exchange-listed firms in 106 economies around the world (http://rmicri.org).  The system also produces the RMI Corporate Vulnerability Index for countries and portfolios of special interest.
The third part of the talk presents a bottom-up approach to credit stress testing that utilizes the CRI infrastructure. Its performance is assessed and limitations discussed using the listed corporates in Singapore and the US.

We consider testing the mean-variance efficiency in the context of a high-dimensional multi-factor model, with the number of assets much larger than the time-series dimension.  Most of the existing tests  are based on a quadratic form of estimated alphas.  Under high dimensionality, however, they all suffer from low powers because the accumulation of a large amount of estimation errors overrides the signals of the true nonzero alphas.  To resolve this issue, we propose a new test that deals with high-dimensional hypothesis testing problems, called “power enhancement”.  A screening statistic is introduced to screen  off most of the estimation errors and consistently select stocks with significant alphas.  We develop a feasible standardized Wald statistic using a consistent estimator of the high-dimensional weight matrix based on thresholding.  In addition, by attaching the screening statistic to the traditional quadratic-form tests, our proposed test significantly enhances the power of the Wald-type tests under most of the alternatives, while keeping a correct asymptotic size.  Finally, the proposed methods are applied to the securities in the S&P 500 index as an empirical application.  The empirical study shows that market inefficiency is primarily caused by a small portion of mispriced stocks, instead of aggregated alphas.  Moreover, most of the significant alphas are due to extra returns (underpriced).  This is a joint work with Jianqing Fan and Jiawei Yao.

We consider the class of local-stochastic volatility models.  In this setting, we derive a family of expansions for the transition density of the underlying, option prices and the associated implied volatility.  The density and implied volatility expansions are explicit (no numerical integration is required).  We test our implied volatility expansion on three well-known models: CEV, Heston and SABR. Joint work with Stefano Pagliarani and Andrea Pascucci.

We study the estimation of moments and joint moments of microstructure noise.  Estimators of arbitrary order of (joint) moments are provided, for which we establish consistency as well as central limit theorems.  Empirical studies reveal (moderate) positive auto-correlation of the noise for the stocks tested, in particular, the noise is not white but colored.  We then study the estimation of the integrated volatility under dependent noise setting.  Our proposed estimator enjoys the optimal rate of convergence.  Numerical studies demonstrate good performance of our estimator.  Based on joint work with Jean Jacod and Xinghua Zheng.